Pokém… j.k.

Anime has a lot of subgenres, so selecting one that represent all is quite unreasonable.
But you might try Ghost in the Shell, Grave of the Fireflies (have not watched that one, but Roger Ebert was full of praise), Higashi no Eden, Serial Experiments Lain, NGE (obviously), Dennou Coil, Great Teacher Onizuka, Tora Dora, and one of my recent favourites, Angel Beats.
If you like Horror/murder mysteries/thrillers, Higurashi no Naku Koro Ni is great, too.

If I had to pick one anime, I’d go with FMA or Trigun.

Hayao Miyazaki has gotta be in there. I’d pick his first one, Nausicaa of the Valley of the Wind.
For the more sci-fi ones, I would second Ghost in the Shell, also Evangelion.
Romantic comedy should go to: Rama ½, second GTO.

Personally though, I would show Cowboy Beebop.

I second Fullmetal Alchemist

Akira, Cowboy Bebop, Fullmetal Alchemist, Ranma ½, Garzey’s Wing, Neon Genesis Evangelion

A crash course in the good, the bad, and the ugly. Remember to keep your friend strapped down while watching Garzey’s Wing to prevent attempted suicide (a fully justifiable reaction).

Cowboy Bebop is spectacular, but I don’t think its representative of anime. Its decidedly in a class of its own.

I agree with Ranma ½, its classic.

For eva I’m torn… again one of my favorites, but I’m not sure its representative.

No single anime is representative of the medium. In order to give his friend “an honest snapshot” that coveys “the overall feel of the medium,” @Nullo will need to represent the diversity of anime as well as show the classics.

@SavoirFaire Of course no single show can actually represent the medium. But, to try to accurately represent it, it makes more sense to use representative shows. I’m not sure I know of another anime that is anything like CBB with respect to animation style, character development, or story telling mode. The closest I can come up with is Samurai Champloo (not surprising as it was made by the same people) and thats still wildly different with respect to animation style and story telling (i.e. its a single continuous story instead of a series of semi-stand alone pieces).

I agree completely with lifeflame. Hayao Miyazaki’s work is what got me into anime in the first place. When I watch one of his beautiful stories, I am swept into worlds where color and detail are practically bursting off the screen and the character’s you come to love will almost always make you feel like a giddy child once again. Miyazaki is pure win! I would show your friend any his stories as a part of a representation of anime along with some other great series and movies like; xam’d, tenga toppa gurren lagann, durarara, ghost in the shell, sword of the stranger, and eden of the east.

@roundsquare But to not show something like Cowboy Bebop would be to ignore how diverse anime is and can be. I worry that a list of “standard issue” shows and movies would risk pigeonholing the medium as a whole, thus I think a broad sampling provides a more accurate snapshot.

Oh, Samurai Champloo is also awesome. Just sayin’

Okay, trying to keep in mind you said Anime and not Hentai

Ninja Scrolls and Ghost in the Shell are great. For a quick lesson, you could point out the background on Oren in the movie Kill Bill Part 1.

@SavoirFaire Thats a good point. I guess it comes down to what @Nullo means my representative.

So I guess I would say show other stuff first (since its a bit more representative) and come to things like CBB later.

Kiki’s Delivery Service, My Neighbor Totoro, Princess Mononoke, Wings of Honnemise, Laputa Castle In the Sky and Graveyard of the Fireflies represent that what is almost the perfection of an anime as a unique medium in full length film format.

In the TV series format, you could go all the way back to the 60’s or 70’s with Voltes V, Mazinger Z and Grendizer as ancestors of the modern, derivative American Transformers of today. If you want very typical anime ( which could not truly represent the whole ) then Cowboy Beepop, Ranma ½ it is amongst hundreds!

@filmfann I guess you are the only one who mentioned Ninja Scrolls. Truly you are a Master! No action anime in my view so far has outmatched Ninja Scrolls when it comes to story build-up, engaging characters and awesome editing!

@filmfann Ninja Scroll is awesome.
I’d have to say that stuff like Neon Genesis Evangelion, Ghost in the Shell or Gundam Wing represent the medium a bit better though. Gotta have big eyes and huge robots and weird machinery and shit, although anime has long disconnected itself away from being defined merely by those aspects. It’s so much more now.

Well, I’ll stand corrected, as the only anime I really like is Ninja Scroll and Sailormoon, so I don’t think I’m very informed on the subject.
Although DBZ was entertaining. Love seeing dudes floating around and yelling all day long.

To really answer this question I think two things need to be addressed. One is, what purpose are you showing anime to your friend for? To get him hooked? To just say, “Oh, this is anime?” To introduce him or her to the history of anime?

As many of people have pointed out, anime is really a medium, rather than a genre per se. It’s a bit like saying, what is the definitive “movie.” There are many subgenres, including sci-fi robot movies to romantic comedies.

So one question I think is worth asking is: When we think of an anime that can “represent” the medium, what qualities are we thinking about? Is it huge eyes and robots?

I would argue that visually distinctiveness is important; and you would need to show something that shows that range. Background score is also key.

I would also argue the complexity of character and storyline, and the ability to go beyond what we think of “normal” in a Western storyline is also key. So whether it is the blurring of good and evil (that’s why I would pick Nausicaa of the Valley of the Wind); the fantastical element; the looser boundaries of sexuality (Ranma ½), that’s quite anime.

I also think the there tends to be subversion of genre. Actually I think that’s quite Japanese – they take some invention from another culture, and they make it their own. You see this, no matter in writing, food, products (e.g., cars). They took the Western face and made it their own. They took the cowboy genre and made it their own. Even Evangelion, for example, is a subversion of the robot genre.

Finally, there’s cutting edge anime and there’s run-of-the-mill anime. Sailormoon, for example, might be “typical” teenage anime fare, but I really wouldn’t show it as representative of what anime can do.

@lifeflame
Well, Sailor Moon is basically the archetype for the mahou shoujo genre.

Another vote for Miyazaki. I don’t really go for anime that much, otherwise.

Miyazaki is truly the master. Love Full Metal Alchemist. Ah, My Goddess…who would have thought this hobby would take over my interest all because my grand-daughter liked Sailor Moon? Inu Yasha, Rurouni Kenshin…Need I go on? And all because of Sailor Moon.

If you’re trying to initiate someone into Otaku culture, imo it shouldn’t involve showing them what anime is as much as what they want to get from it. My friend’s gateway anime was Chobits, which fits into his obsession with computers (he’s going to major into computer engineering), and Nodame Cantabile fit with how much I liked classical music at the time (although I honestly got more than I bargained for in the romantic comedy aspect of it. If my friend had advertised that part of it I might never have started, but I enjoyed it more than I’d have thought). The thing about “generic” anime, or trying to represent anime in general with a single one, is that they tend to be Shounen or styled similarly, while not everyone is going to be a huge fan of adventure-style anime in the long run. I’d say show them something related to something they already liked, and if they like it enough they’ll stick around for more.

As for what makes anime generally good, personally I’d have to say it’s the occasional weirdness of show premises coupled with strong character archetypes and good humor. Try to focus on something like that (and on that note I second @ragingloli‘s Angel Beats! recommendation).