First: It has high production values and the director wasn't screwed by a committee, so he could tell a coherent and finished story.
Second: It's accessible. It I want to hook someone on anime (or gently take the anime virginity of someone) I show them Cowboy Bebop. It has archetypical characters that everyone can relate to yet they're fleshed out in the story and grain gravity as authentic characters.
Third: No fan pandering, genre shit. (To watch this show you don't have to be into moe, mecha or any other subcultural movement of the decade)...though being familiar with John Woo choreography helps.
Fourth: It's whimsical and light, the show never takes itself too seriously and it is jam packed of cultural references that - unless you lived under a rock for the last *20 years* - you should *get*. It still can tell moving or insightful stories, and when it finally tries to do drama or tragedy it still has an air of brevity about it, that stylized "jazz of storytelling" that entertains and makes you feel welcome from the get go... and still do some heavy shit, not pull punches and make us feel for our heroes.
Five: The music, the music. Yohko Kanno has never been so good ever since. This and Escaflowne were her masterpieces that she has yet to top. Light, whimsical and badass, serious at the same time. Just like the show.
Cowboy Bebop
Berserk
School Rumble
GTO
Full Metal Panic
Ouran Highschool Host Club
Toradora
Cowboy Bebop because it is freakin Cowboy Bebop
Berserk same as above
School Rumble because it made me laugh hard and not many animes do that.
GTO because I love Onizuka as a character.
Full Metal Panic because it gave me a lot of epic moments to remember. The first season was pretty bad, I'll admit.
Ouran because it showed me that it was ok to watch that kind of stuff.
Toradora for being a romantic anime where the lovers actually admit there love to one another and embrace there relationship by the end of the series, not leaving the relationship ambivalent.
I'd choose Full Metal Panic as a fluctuating favorite because it gave me the most "chest swelling" moments. You know, that feeling you get when something really epic/touching/awesome happens in an anime.
1.Samurai Champloo-favorite series, luv the soundtrack
2.Full Metal Panic-Fumoffu was probably the funniest series I have seen in a while
3.Bakemonogatari-I love Hitagi, she is so cute.
4.Gurren Lagann-Only the 1st season, 2nd wasn't as good
5.Ergo Proxy
6.Natsume Yuujinchou