You Knew It Was Coming.

Great Anime, of course!

• Cowboy Bebop: All style, not so much substance, and we do not care. Most episodes in this cowboy/bounty hunter in space thingamajigger are stand alone, but they build, too. They do humor and angst with equal confidence. Deep characterizations, an awesome jazz score, parodies of Alien, Batman, blaxploitation movies, etc... It's kind of Tarantino-ish, now that I think about it. Plot: motley group of space bounty hunters in the future look for bounty, and generally fail.
  

• Kodomo no Omocha: Hilarious show for the young-adult set. Very very funny and sweet, but super quick dialogue and puns flying fast means it's not for the first-time anime viewer. Plot: Kid star of after school special-type show learns to grow up as a pre-teen.
  

• Neon Genesis Evangelion: I didn't get it so much the first time. Not for the fainthearted. Let's say, it's the Ulysses of anime. Robots, Freud, pseudo-religious claptrap. Sadly, Shana identifies with Shinji. But loves Misato! Best female anime character evar! Plot: "Angels," these big alien things, drop onto Earth (particularly Japan) to lay waste. Only robots piloted by weird-ass 14-year olds can stop them for some reason.
  

• Rurouni Kenshin OAVs: Trust & Betrayal: Beautiful, chock full of enough symbolism and leitmotifs to make an English major's heart warm. But it certainly helps to be okay with violence and to have some background in the Meiji Restoration. You don't need to see the series to see the OAVs, though it makes things more fun, of course. Plot: Backstory about our favorite pacifist samurai, Himura Kenshin, as he grows up from widdle boy to cold-blooded assassin to the soft-spoken hero we know and love today.
  

• *Spirited Away: My favorite; see below. Plot: Girl ends up in alternate wonderland-esque world, works in a bathhouse, tries to save her parents who have been turned into pigs.
  

• Vision of Escaflowne: Possibly the most fun anime series of all time. It's got something for everyone: robots, a magical girl, a catgirl, philosophy, a steampunk/clockpunkish setting, EXCELLENT music, dragons, tarot cards, bad guys who scream "Burn! Burn!!" I love ALL OF THESE THINGS. Plot: Girl track star and tarot aficionado from Japan ends up in an alternate universe and must use her crazy mystic powers to save the kingdom from evil Nazi empire (with robots).
  

• Whisper of the Heart: Miyazaki, but not fantasy. See below for details.
  

Good Anime

• Castle of Cagliostro: As I said below, get past it's 70s-ness and you will see the gem inside. Don't take it from me; it's also a Roger Ebert favorite.

• Fushigi Yuugi: Okay: is it good? Depends. Is it, like, deep? Uh, not so much. Is it sometimes annoying and/or over the top, in classic 90s anime style? Uh, sometimes. But is it the most addictive show in existence? Oh lord yes. The plot is fun, the characters are fabulous, and the humor actually humorous. Go in expecting little, and you will be very pleasantly surprised. Plot: Girl from Japan drawn, Neverending Story-style, into a book about a fantasy world based on Ancient China; must become a magic priestess to save the world.
  

• Great Teacher Onizuka: Okay, kind of cheating, because I didn't actually watch the anime; I watched the live action drama. But it is fun! Plot: a former bike gang member decides to become the Greatest Teacher in Japan. Amazingly, something about teachers that I DO like! Maybe because it's so ridiculously unrealistic that I can get past the genre for once.
  

• Last Exile: Hard to understand because I got a bad fansub, but it's beautiful steampunk about AIRPLANES! with cool characterization and a fun, if slightly convoluted plot (though, again, it might have been the subtitling).
  

• His and Her Circumstances: My vote for best shoujo/romantic anime. Well, the first half. Then it gets dumb. Made by the same guys who brought you Evangelion.

• My Neighbor Totoro: See below for "WAI WAI ^_^"-style gushiness. It's cute. Deal.
  

• Princess Mononoke: Violent, sometimes hits you over the head with MESSAGE!!!, but we still love it. It's more complicated then you may think at first.
  

Fun and Possibly Worth Watching, If You're Into That Sort of Thing

• Ranma 1/2 TV: Unadulterated silliness. Funny, though. Plot: Um, ninja family turns into various creatures when doused with water? Yeah, that's it.
  

• Rurouni Kenshin TV series (up to and including the 2nd [Kyoto] arc): If you like your Meiji-era samurai with a dash of X-Men-type powers... Plot: Pacifist samurai faces his non-pacifist past in 1870s-ish Japan.
  

• Trigun: More futuristic cowboys in space? What is WITH this genre?

Seems Good, But I Haven't Seen Enough to Judge

• Crest of the Stars: Very, very good so far. I just keep forgetting to finish it. It's cold, hard sci-fi, of the old kind. And it's based on--shock! awe!--a novel. Amazing.
  

• Full Metal Alchemist: The episodes I saw (maybe five of them, not in order), had a LOAD of potential. I need to see them all in order before I can judge.