It's not my all-time favourite but one that I've heard recently and got stuck in my head in the K-ON! ending. I did a quick search of the thread and it seems it's been mentioned but not posted.
The Akagi ED also stands out. I don't really like the "Raarrrghhh" bit but it's cool how it's being used for an anime about Mahjong.
The first One Piece ED is a very "pretty" song.
And after you've been made quite melancholic by that One Piece ED, listen to this one.
The 2nd Death Note ED was also something to look forwards to after the series went downhill, despite more stupid "raargghh!" stuff.
And the more clever and mature sounding Death Note ED from back when Death Note was clever and mature.
Finally an actual song by a band that people will have heard of without being anime fans. The Ergo Proxy ED - Paranoid Android by Radiohead.
Sorry for any repeats, but a lot of people don't say what their songs are in text and I don't want to go through and watch every video to see if I'm duping.