Maybe one of the best 2D games in that times.
Jazz Jackrabbit was one of those, and while I didn't purchase the first one I remembered playing the demo from when I was a kid. When I spotted Jazz Jackrabbit 2 for 10 bucks in the bargain bin, I yearned (that's right, yearned) for those days of afternoon fun side-scrolling action.
JJ2 delivers on that and more. The game was designed to run in Win95 and I was able to get it to run on WinME (I assume XP should run ok). The graphics seem a little dated, but it does all of its work on very little hardware resources (this is a sprite-based engine after all). JJ2 takes you through several different worlds with drastically different tilesets. Each level has its own identity and pretty hip soundtrack.
Gameplay is pretty straight-forward. Jazz or his brother Spaz are your two selectable characters. Jazz has faster speed, and Spaz has this helicopter move with his ears (as I recall). Your primary weapon are guns with different ammo and characteristics (I think about 6 in all). There's coin-collecting (jewels as I recall) and other platforming elements that transition well.
You get the speed and crazy level design of Sonic, with the music and humor of Gex, and the side-scrolling of Rayman. Cool, eh? Definitely worth you checkin it out.