If you liked Air TV, I recommend the Air movie (more mature, not as confusing ending), and Kanon, by the same creator.
As for other anime.
If you have time on your hands, watch Monster. It's 74 episodes long, but an amazingly realistic thriller, a great plot, no filler episodes at all.
Bleach is great but be sure to ignore ep 63 - 109, that filler arc is just terrible.
I also recommend Beck, about a 15 year old boy that starts playing in a band, great and realistic teenage series. (without the retarded sweatdrop humor)
Wolf's Rain has a great atmosphere and is worth checking out too.
Elfen Lied. A lot of blood and gore and nudity, but the story's awesome.
I second Samurai Champloo, Neon Genesis Evangelion and Death Note. All great series, even though the latter one is still on going.
I've watched a lot more but I can't particulary recommend them. (like Chobits, didn't really like it)