But first off, some generic Anime terms that are important or useful to understand.
Anime: While in Japan, it refers to animation in general, in other countries it refers specifically to the animation style of Japan. The topics, genre, and aim of the series are highly variable. The age category of the viewers is likewise designed to range from children to young adults and hitting everywhere in between.

AMV: Anime Music Video. These are fan videos which take either one or several anime and place the animation to music. They are considered by many to be an artform to themselves. See animemusicvideo.org for more info.

Bishonen/Bishoujo: Beautiful boy/girl resp. These are specifically characters who are designed to be attractive. Bishonen characters are normally drawn with feminine frames, while bishoujo characters are normally physically attractive characters who are young in age.

Doujinshi: This is a fan based work that is normally put into a manga format. However, the actual range is anything from manga to video games.

Eroge: A game in Japan which features sexual content, usually as anime. This is found very often in the Visual Novel format, hence the association.

Fanfiction: Fiction written using characters from the intellectual property of an established plot and universe. The authors do not claim rights to the characters, but use the story as a means of expression or as a means to manipulate series as they wish it to happen.

Fansubs: These are fan based creations in which an individual or group will take an anime in an unedited Japanese recording (called a RAW) and will translate the dialogue and place subtitles with a video editor. While they are often considered a ‘gray area' of legality, websites which distribute these will cease if they receive a request from official distributers.

Harem Anime: Despite the sound, it is normally not a single character having sexual relations with numerous others. It is instead normally a single character (normally male, but not always) who is being romantically pursued by numerous members of the opposite gender. It is usually within the realm of reason (4-5) but some can get utterly ridiculous in number (see Maho Sensei Negima).

Hentai/H/Ecchi: Hentai is Japanese for Pervert. These are all different terms for sexual content which features anime style characters. They normally have different associations. Hentai is normally ‘hardcore' in nature, while H content is normally found in games. Ecchi is mostly associated with softcore, sometimes non nude, content. Also, all of these are the reason to put on safe search whenever you are using Google for anime images -_-.

Magic Girl: A character who is a normal girl, often a student, who will transform into an alternate persona in order to fight whatever happens to be the villain of the series.

Manga: Manga is a Japanese type of comic or graphic novel. They are almost all in black and white inked drawings, and a good deal of anime is based off of these (or the other way around).

Mecha: Giant piloted humanoid robots. Many anime focus upon these mecha and their pilots.

Otaku: Japanese for Nerd. The implications in America is someone who really likes anime or other Japanese media forms. It has a much more negative connotation in Japan.

Scanlations: The same process as fansubs, but with manga instead.

Seiyu: Japanese word for voice actor or actress.

Shonen/Shoujo: These refer specifically to anime which is aimed at boys and girls, respectively. They often feature an underdog type character of the respective gender who nevertheless rises to become equal to or surpassing their superior rivals.

Subs: Subtitles. A good number of anime connoisseurs will only watch anime in the original Japanese with subtitles. The reasons are varied, the most often heard reason is the superiority of the voice actors in Japan.

Visual Novel: This is a form of video game in Japan. They are very much akin to a choose your own adventure story such as those found in books in the USA. They normally feature a background picture with characters in the foreground whose expressions change as their mood does. Text is usually displayed in a box at the bottom of the screen with choices to make at intervals. They are associated normally with Eroge games (see above), but are not necessarily all erotic in nature.

Yaoi/Yuri: Homosexual relationships, male and female respectively. May or may not be sexualized.

These are basic terms, and will often crop up in forums. I find knowing the ‘naughty' terms helps for purposes of avoidance tactics (though I purposefully avoid telling some individuals ^_^).

 

This is a compilation of some of the anime that I have really enjoyed over the years. I have been watching anime now for over half my life. The first I ever saw was Tekkaman, followed by My Neighbor Totoro. While most of these are easily findable and hardly rare, they are great for those looking to get into the anime experience (or parents who have absolutely no idea what their kids are talking about).

10 Anime That You Absolutely Must See:

1. The Films of Hayao Miyazaki
   
   
   

   These are my main arguments for the concept of anime as art. My Neighbor Totoro was one of the first anime I had ever seen. The tape kicked the bucket long since, but I still fervently follow Miyazaki. He is a truly phenomenal artist. The two that I recommend above all others are Spirited Away and Totoro. Howl's Moving Castle is significant as well, and is especially fun when you realize Christian Bale is the voice actor of the main hero. As for Totoro...well, look at him! How can you not love the giant raccoon/squirrel/panda hybrid?

2. The Films of Makoto Shinkai
   
   
   

   This man is a genius. He has been hailed by many as the next Miyazaki, and I fully agree with them. His first breakthrough, Voices of a Distant Star, is a sentimental, heart tugging piece. It becomes more impressive upon the discovery that he did the entire piece on his Macintosh home computer, with only himself and his fiancée as the voice actors and his friend composing the music. I especially recommend 5 Centimeters per Second. It is a down to earth, brilliant story of love, friendship, and separation. It also has the dubious honor of being one of the few anime that I have written a fan fiction for.

3. Mobile Suit Gundam
   
   
   

   Gundam has become almost eponymous with the concept of a large human robot with large guns and a beam sword. The original work, Mobile Suit Gundam, is a decided classic of the anime world. It has since seen several sequels and spinoffs. The first set I watched was New Mobile Report: Gundam Wing, which I still feel is one of the better of the spinoff titles. The only other spinoff that I have had much fun with was Mobile Suit Gundam SEED. I, along with many fans, site this as possibly the best spin off of the series. Gundam SEED is the other anime with a dubious honor of being good enough, yet incomplete enough that I wrote a fan fiction for it. The most recent title is Gundam 00, which, aside from sounding a little too James Bond, is one of the more favorably received, with a second season currently in the works. I recommend beginning with Mobile Suit Gundam, unless you find the animation too old fashioned, in which case I cannot recommend Gundam SEED highly enough.
   

4. The Melancholy of Haruhi Suzumiya
   
   
   

   This series is often one of the first recommended on internet forums, and for good reason. The anime is a good example of a series that does it right. The humor is witty, the story is compelling and quirky, and the characters are all wonderfully unique. It is not serious in any real way, though it can fool you at times. This is another anime that experimented, in this case with the Light Novel, a short novel with pictures added in for effect. This is an amazing series and I agree with people who say to watch this when hunting for a new anime.

5. Last Exile
   
   
   

   I'm not sure how popular this is on the net, but it was one of my personal favorites. The setting is unique, something that most anime don't strive for, in a steampunk world of airships and a war that has continued for too long. The characters are interesting, the plot is compelling, and the animation and the way CG and hand drawing works together in this series is well worth the purchase.

6. Rurouni Kenshin and Samurai X
   
   
   

   I class these as one set because they are all really just one long series. Trust and Betrayal are the initial story, then Rurouni Kenshin, and finally Reflections. This is the series if you want sword action. But it's more than that. It is a real look at the quality of the human condition and how far one man would go to seek redemption. It is a beautifully told story, with the action complementing the story rather than being the focus.

7. Gankutsuou:The Count of Monte Cristo

   
   
   This is a series which I picked up on a whim and fell in love with. The story of the Count is retold in a space opera setting. Before you think "what the hell," pick up at watch the first episode. The series has a few hallmarks, including a unique animating style, a decently accurate retelling of the Count of Monte Cristo, and despite the fact that you can likely see the plot twists coming, they will still throw most people for a loop.

8. Ghost in the Shell
   
   
   

   This is one of those anime that takes a while to get your brain around. Quite aside from being complex, it is a real revolutionary piece. One of the classical dystopian stories of control, human advancement, and the relation of humanity and technology. Note that the movie does have spattered periodic nudity as the main heroine's cloak doesn't work through clothes... Other works by Masamune Shirow are likewise quite good. Appleseed is another one that I would recommend if this movie fails to confuse you.

9. Fate/Stay Night
   
   
   

   This is a wonderful anime based off of a visual novel. The story is compelling and complex, with characters that I absolutely fell in love with. It has a great blend of humor, action, romance, and drama. It is something of a cult hit (the cult being anime lovers.). Absolutely brilliant.

10. Final Fantasy 7: Advent Children
    
    

    Where do I begin? This is the sequel to the game Final Fantasy 7 for the Playstation. It is a completely original work and it took years to develop it. It has the best CG animation this side of Pixar and the characters are amazing. The fight scenes are also spectacular.

 

Honorable Mention: Full Metal Panic

It's hard for me not to love on this series. It has a lot of humor, a lot of action, cutting edge animation, and a story that strikes me as either the most brilliant or the most stereotypical I have ever seen. I highly recommend watching it, but only if you like action.

Series not yet completed That I Still Recommend:

These series have not finished yet, but I still enjoy them immensely and I think other's might as well.

Bleach: This is a fun series, with enough twists and turns to leave me dizzy. I might recommend the manga over the actual anime, as the added scenarios in the anime (fillers) can get exhausting and confusing. However, the plot itself is compelling, with the normal shonen cast of characters that bounce between funny and serious depending on the situation at hand. The characters are varied, but most are not especially deep.

D. Gray Man: This is a funny little anime I picked up in manga form first. This anime so far has been amazing. The characters are well thought out, the action is top notch, and the plot twists keep me on a roller coaster through the whole thing.

Hellsing OVA: This is complex. There is a completed Hellsing anime that finished some time ago. However, there is a new series called Hellsing Ultimate with updated graphics, more manga-accurate storyline, and featuring a bit more in terms of character development.

Anime I have not seen but come highly recommended:

• Chrono Crusade
  
• Code Geass
  
• Fullmetal Alchemist
  
• Galaxy Angel
  
• The Girl Who Leapt Through Time
  
• Ranma ½
  
• Robotech

Anime for Fun: This section is dedicated to anime that, while not particularly deep or motivational, I still found immensely fun.

Vandread: Two planets locked in a war, one composed entirely of men, the other entirely of women. And this is the plot launcher. While it sounds like the setting for a hentai show, hold that inner critic. Yes, the show uses crude humor a lot, but the general ignorance of the characters involved just makes it that much more hilarious. Lots of action, lots of boys being boys, and girls having fun. Again, not deep, not something I would recommend to critics, but a lot of laughs.

Mahou Sensei Negima!: Allow me to say that this is a cute anime, though it can be classified nicely as a bit immature, and at worst as downright crude at times. Ignoring the fact that there is a middle school class full of girls who are a bit too eager to remove their clothes for their ten year old teacher, the series is a lot of laughs. Thirty students with quirky and funny personalities, and Negi, the titular character following in his father's footsteps makes for one fun anime.

Lucky Star: This is a cute little anime. Very funny, but I recommend watching other series first to better understand the humor that goes into it.

Azumanga Dioh!: This is a hilarious anime following the lives of a group of girls. To say the least, they are a unique bunch, keeping the teachers out of it even. The show is really quite pointless, with very episodic scenarios. It is amazingly funny and I still point people here for when they need a good laugh.

School Rumble!: This series actually rates rather high on my list, though it is really just a barrel of laughs. It is mainly a parody of...well, most everything, actually. The issue with me saying I don't like parts of it is that they may overemphasize parts that most people don't like. Amazingly good, comedic from start to finish.
Caramelldansen: Just go to youtube, enter the title, and enjoy the frames of animation these provide.

Anime to Understand Anime:

Dragonball: This is not actually high on my list of good anime, but it's hard to argue against the overall importance that the anime has had on North American audiences especially. For a quick summary, Son Goku is an alien called a Saiyen living on earth. The series follows his various fights, adventures, and more fights. If you ever wonder why some characters have glowing yellow hair, it's very likely due to this series.

Naruto: Naruto is quickly becoming the new shonen series to follow. I followed the anime up until they decided to take a year or two off from the manga's story and create their own subset. This is the inspiration for ninja-esque anime. I still continue to read the manga, though even that has begun to gradually lose appeal.

One Piece: Oh yes...the pirate anime. I find the animation a little annoying, and the fact that the cast is extensive to the point of idiocy, not helped at all by the fact that all the characters stay alive. I find it tiring to continue watching (or reading) this particular story. Still, it has mass popularity, and if you like quirky, this is it.

Inuyasha: This one I actually rather enjoy and it's educational. Everyone wins! The series will give a lot of the stereotypes for animes that continue to crop up, in particular character archtypes.

Games to Understand Anime:

There are a select few video games that are really helpful in knowing if you will enjoy anime. Not only that, if you like anime, you'll probably like these.
Metal Gear Solid: This series has spanned every platform except the X-Box and recently released its final installment for the Playstation 3. It features one of the most in depth cast of characters of any media I have ever seen. The cutscenes are lengthy, and the story is told mostly through them. Solid Snake and his merry band have attained status among gamers that is legendary. Try it out. There are worse ways to spend your time.

The Tales Series (Tales of Symphonia, etc): These feature characters which are very anime-esque. The style, story and everything all feel like anime to me. I particularly enjoyed Tales of Symphonia, which, ironically enough, has its own anime series that is currently going on. Play these if you find yourself enjoying the anime.

JRPGs:

Japanese RPGs. Simply put, any RPG to come from Japan. I would hit up Final Fantasy at least in order to understand the hype a little better (or put it into perspective).

Manga vs. Anime:

A question I get asked a lot is do I like manga or anime more. To be honest, I often side with manga over anime, but then I'm a student of literature and like to read. Generally speaking, manga has a tendency to be the storyteller's intended story without addition or reduction. Anime, on the other hand, has a soundtrack and is easier to watch for long periods of time (both of which I consider positives). Generally speaking, manga is released before the anime, though this is becoming reversed in some cases, and may continue after the anime ends, Inuyasha being a good example.

There are also some differences in which the series completely differs based on which media one is indulging in. The best example I know of is Full Metal Alchemist, in which the manga and anime go in completely different directions.

In the end, I feel that each has its own benefits. But there is no manga form of 5 Centimeters Per Second, so I will always have a reason to see anime.

In conclusion:

Anime is without a doubt one of the single greatest influences on me as a person. Some basic lessons like never give up and respect yourself for who you are can be found in them, while also being genuinely entertaining and occasionally seeking at even deeper meanings. I hope this list can help you out.

Note: I take no credit for the pictures. I found them through Google.