Hack//sign. Evangelion (Stay away from Rebuild though, it dumbs it down way too much).
Blassreiter.
Azumanga Daioh.
Lucky Star. Clannad (Definitely, only anime to bring me to the brink of tears).
Air Gear (Screw everyone else, I like it, they discontinued the anime but the manga is still going).
El Cazador de la Bruja.
Noir.
Angelic Layer (If you can find it).
Cardcaptor Sakura.
Baccano! (Good selling point of this anime is that there isn't any one main protagonist, they've all got a story).
Blue Gender.
Big O.
Mai Hime.
Haruhi Suzumiya (During the second season, after you watch the second episode, skip right to episode nine, because 3-8 are all repeats of episode 2, literally the exact same things happen, right down to identical dialogue, there's a reason, just not a very good one)
Blassreiter.
Azumanga Daioh.
Lucky Star. Clannad (Definitely, only anime to bring me to the brink of tears).
Air Gear (Screw everyone else, I like it, they discontinued the anime but the manga is still going).
El Cazador de la Bruja.
Noir.
Angelic Layer (If you can find it).
Cardcaptor Sakura.
Baccano! (Good selling point of this anime is that there isn't any one main protagonist, they've all got a story).
Blue Gender.
Big O.
Mai Hime.
Haruhi Suzumiya (During the second season, after you watch the second episode, skip right to episode nine, because 3-8 are all repeats of episode 2, literally the exact same things happen, right down to identical dialogue, there's a reason, just not a very good one)