Tatami Galaxy
Kaiba
Kuuchuu Buranko
Mahou Shoujo Madoka Magica
Kuragehime
Ef - A tale of Memories
Ef - A tale of Melodies
Baccano!
Durarara!
Kanon 2006
Haruhi S1 and S2 (though S2 isn't to everyone's taste, but you'll want to watch it to fully appreciate the movie)
Haruhi Movie (very awesome)
Paprika
Bakemonogatari
Eden of the East
Mushi-Shi (finished airing in 2k6, still counts!)
Noein (same as with Mushi-Shi

)
Kemonozume
Dennou Coil
Mind Game is from 2k4 so hence why I don't have it here, but I'd recommend it anyway. ┐( ̄ー ̄)┌