Oh god, so much choice. I will just list some of my favorites here, along with a youtube link. More may follow later:
Great Teacher Onizuka OP1:
Done by l'arc-en-ciel, which is a band that I really like and for me this is their best work. I really like the gritty yet fluid animation here, plus the laid-back style
Overman King Gainer
Shut up, okay! I like the silly dancing! I have no idea who had the idea to make such a silly OP, but I loved it.
Cromartie High School
Cromartie is a really weird deadpan comedy, and this opening fits it perfectly. I really like the song somehow, but it's just plain weird with all of the ufos, gorillas and tanks rolling along the screen.
Kachou Ouji
This is a very peculiar series (about this middle aged guy who was a former rock-star and who has to save the earth using hard rock), and it also has a very peculiar opening, which just perfectly captured the intoxicated lifestyle of your average rockstar. Plus, I really like the experimental animation here.
Sci-Fi Harry
Warning: this is a rather disturbing opening. Nevertheless, I can't recall any other opening that had better and more expressive animation than what this one has. It looks completely unlike any other opening I know of as well.
Paradise Kiss
Paradise Kiss is about a bunch of fashion students, and it shows: this opening is incredibly stylish, and it's full of awesome visual ideas. Not to mention that it has a killer song here.
Ergo Proxy
Another incredibly stylish opening with really good images and visual effects. It's also one of the few openings with actually good English there.
Uchuu Kyoudai OP 1
A series about space travel, this opening perfectly encapsulates that, along with being completely silly with the rainbows and all. The rock song is also really good here.
Kamisama Dolls
I really like the singer of this song, Chiaki Ishikawa. She really delivers here, and together with the really creative visuals make this a really good opening.
Bokurano
Again, Chiaki Ishikawa. Awesome singer. This is one of those openings that tells you A LOT about the characters. It contains a lot of hints, but you're only going to get them once you watch the series.
Bounen no Xamdou
Bounen no Xamdou is one of the most polished action series that I have watched, and this opening again really shows this. Great song, great animation, great style.
