Obvious favorite opening is obvious, but I didn't see it mentioned yet, sooooo:
Then there's the Baccano! one mentioned in the first post (which is almost a rip-off of Bebop's, but Bebop's is a rip-off of others so..)
Speaking of which, I also truly enjoy most Lupin III openings, but this one is probably my favorite yet; so sleek, so stylish, so great.
And the Samurai Champloo opening is pretty much perfection for the series (the ending was already mentioned in this thread, I'm glad to see).
One series I haven't watched in probably ten years is FLCL, but I still get this song in my head from time to time:
And a somewhat similar one which I don't think gets enough recognition in threads like these:
There's so many more, of course, but I guess five is enough for one post.