I'm biased, but pretty much all of Sonic 1, 8-bit version (including the ending) and the first level of Sonic 2. It's some of the best music I've heard come out of a 3-squares-plus-noise PSG chip outside of the demoscene (or a Mad Max / Whittacker / Dalgliesh scored game, which is practically the same thing), even though it's both simplistic and short. Whoever it was on Sega's team who wrote it was a genius at coming up with a unique, fitting theme for a particular level, then capturing it within pretty harsh hardware and data storage limits.
Just went and listened back to them all on youtube, and though with the rose tints removed they do seem a touch unsophisticated, they're still good pieces of music. The Scrap Brain metal remix posted further up the page captures what we heard in our minds whilst playing the game quite effectively, too.
The Genesis ones never flipped my switch anywhere near as much for some reason. Same effect with Streets of Rage. Somehow the 16 bit mixes felt hollow and lazy in comparison.
Oh yeah and the full length version of the intro-type remix of Sonic Boom is an automatic shoo-in.
