Lets see, my personal picks would be:

Gensomaden Saiyuki: An anime adaption of the old story "Journey to the West." Funny, good action, very good drama. Stay away if you don't like anime that involves characters actually occasionally dealing with their pasts.

.HACK//SIGN or .HACK//Legend of the Twilight: Good if you like .HACK to begin with, but some people think it's a little too slow. SIGN is Drama/mystery/little bit of action, while Legend of the Twilight is similar, but less drama and more comedy. (I haven't seen both all the way through though, so if that suddenly changes in either, don't hold it against me.)

I second Ouran High School: [B]Very[B] funny. Only watch it if you like shoujo though, this isn't an anime with tons of explosions.

Fruits Basket: Rivals Saiyuki as my favorite Anime. A shoujo drama/comedy/Underlying Romance about a girl living with a family that are cursed to turn into the animals of the Chinese zodiac when they are embraced by a member of the opposite sex and how she helps them and everyone else around her deal with their own personal scars. Stay away if you don't like sweet (In the awww sense) anime, or anime with powerful emotions.

Ranma 1/2: The classic Action/Comedy. There is a reason this anime has been so popular for so long. Rumiko Takahashi doesn't get any better than this if you ask me. (No, I'm not huge on Inuyasha, it's ok, but not great in my opinion.) Stay away if you like hardcore, deadly, gory action. Or if you have young kiddies around, as there is lots of toplessness.

Anything by Hayao Miyazaki: Enough said.

More to look at but I'm too lazy to write things about:
Cowboy Bebop (Action/drama/bit of comedy)
Gundam Wing (Action/Drama)
Samurai Champloo (Action)
Naruto (Action/Bit of Drama)
Haibane Renmei (Drama)
Love Hina (Comedy/romance)
Full Metal Alchemist (Little bit of everything)
Gokusen (Action/Drama/Comedy)
Noir (Action/Drama)