I do not care for the anime, but the first opening of Bleach, "Asterisk" by Orange Range, stands out to me. My personal favorite, though, is "Moonlight Densetsu" by DALI, the first opening of Sailor Moon. To this day, the song will not get out of my head. The anime has always been a part of my life and so has the music.
Blood+, Serial Experiments : Lain, Soul Eater, Mushi-Shi, Witch Hunter Robin, Ghost in the Shell : SAC + 2nd Gig ... all of those had fantastic openings. Oh, and Ao no Exorcist. I love UVERworld, haha.