Mmm, way too hard to pick my favorites, and I know a lot of my "favorites" really shouldn't be (Lucky Star, for example... -_-), but...
Nostalgia, chronological order, and level of escapism distort my vision too much.
Hmm.
Holy Trinity (You Never Forget Your First): Code Geass, The Melancholy Haruhi Suzumiya (Say what you will about the anime, but the LNs are brilliant), Azumanga Daioh
Secondary Trinity (Shows that are at least as good as the Trinity): Angel Beats!, Paranoia Agent, FLCL
Really, Really Good (Shows that I care about a month after watching): Higurashi no Naku Koro ni***, K-On!*** (Animation-wise, it was pretty solid. And I really needed fluffy escapism that year. Also, the music redeems it), Touhou: Mosou Kakyou (Considering the fact that it's made by a circle of fans... Yeah, it's pretty good. Episode 2 has been announced!)
Worth Watching Once (Good shows that lack anything meriting a rewatch): Serial Experiments Lain, Lucky Star, Ghost in the Shell: SAC, Read or Die, Death Note**, Hayate the Combat Butler*, Detective Conan*, Pokemon (First season was the Shi'ite), .hack//SIGN, FullMetal Alchemist* (Enjoyed the manga more, never finished either), R.O.D. The TV*, Tantei Opera Milky Holmes
Why Did I Watch These?: Nuku Nuku (Quit three seconds in. Holds the record for the fastest-dropped anime I've ever seen), Shattered Angels, Steel Angel Kurumi, Disgaea, Dokuro-chan
*Unfinished
**Dropped
***Season 1 finished