Seconding props for Hemisphere. Best thing about RahXephon! Key's opening is also badass. I love Miho flipping the bird and then ripping her face in half.
I'm surprised Ghost in the Shell hasn't been mentioned yet.
Inner Universe from the first season is great, but I can't see much topping the second season's
Rise. Annoyingly, I can't find either OP on YouTube (though the music itself is all over the place).
Ergo Proxy deserves mention for good, atmospheric openings. I love how the singer belts out "Save me!" over an image of Vincent screaming at the sky. Nicely encapsulates the struggle to bring meaning to a life spent in the show's mechanized dystopia.
http://www.youtube.com/watch?v=4oT2W3gaUBcTsukihime OP/ED for prettiness of all kinds. I love how the OP introduces the characters, spacially together but all stuck in their own little worlds of desperation. It also has Arcueid.
OP:
http://www.youtube.com/watch?v=EQFPQo1cD7cED:
http://www.youtube.com/watch?v=OPOMQkU699c&feature=related~
EDs that work for being diametrically opposed in tone to that of the show itself:
Now and Then, Here and There. We come off half an hour of brutality and madness only to finish with...a gentle, poignant lullaby playing over still screens of everyday scenery. It's a jarring contrast, but that's what makes it work. Now and Then, Here and There is not, at its base, a cynical show; plenty of terrible things happen, but the value of persistence in the face of misfortune is constantly reinforced. (I also can't help but view the ED as a little remember from the producers: youth may have you convinced that your common, ordinary life is trite, but sometime, somewhere, you'll miss all of this).
I imagine the ED doesn't have the same impact if you're not seeing it right after the show. But to me it's beautiful.
http://www.youtube.com/watch?v=bLwWZ7wDaHQBlack Lagoon's ED is an amusing fakeout. Violent sociopath Revy walks along a beach to the sound of calm, steady synthesizer music dripping with remorse and regret, dropping her guns along the way, and for a moment we might be fooled into thinking we're seeing the human side of her at last...then the last couple frames happen and we actually see her expression.
http://www.youtube.com/watch?v=J3_YE9hZRRA&feature=related~
Of course, any discussion of ending themes is incomplete without
So, You Are Going to Eat Me. This one's for Sopko!
http://www.youtube.com/watch?v=61GFr8fVs6g&feature=related