Crash Bandicoot would be my recommendation. I would recommend the ones that Naughty Dog made because after they let it go, I think the series went rather downhill.
Crash Bandicoot
Crash Bandicoot: Cortex Strikes Back
Crash Bandicoot: Warped
Crash Team Racing (PS1 Mario Kart)
I don't have the first one, but I have the other ones and I love them. I still go back and play them from time to time.
Also, If you want a disturbing kind of platforming game, there is Heart of Darkness about a boy who's dog gets kidnapped and his adventure to some shadow world place. I say disturbing because you can die in many interesting ways.
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They may not be platform games, but Metal Gear Solid, Dino Crisis 1 and 2 (mainly 2), Castlevania: Symphony of the Night, and the PS1 Final Fantasies (7, 8 and 9) would be a good honorable mention for good games to get.
