Spyro: Year of the Dragon. It's the first game I remember owning, second I remember playing, and best platformer I've played. If you can get hold if it, and a PS1 memory card, you should. It's got a colorful art style, and the old graphics enhance the charm of it (For me, anyway). You can pretty much count on the other two to be pretty much the same, but YotD is my favorite. It's playable on the PS2, with a PS1 memory card, which you can snag off'a Ebay for about $5.
Another series I liked when I was younger (And would still play, if I could find my copies of them) are the first two, or three Harry Potter games, specifically for the PC. Their not really deep, or even exceptionally good games, but when I was younger, I absoloutely loved them.
And, the final game from my early childhood: Commander Keen. It's an old platformer series from the early 90's, and is probably my favorite 2D sidescroller. I'm pretty sure their free, if you just google them.
EDIT: I just saw @RaphaelsRedemption post, and was reminded of Hocus Pocus. I can't believe I forgot about it. That game was awesome.
Got really hard towards the end though, if I remember correctly.