SPYRO THE DRAGON / Sony / Playstation 1
Crash Bandicoot was Sony's overt attempt to mold a platformer "mascot" to compete with Mario Mario, but the actual platformer game they brought out that most closely resembled Mario's charm and style was Spyro the Dragon. It was also the better game overall.
That said, it was also more specifically made for young kids. It's also much more a hub-world collect-a-thon style platformer, which aren't everyone's bag. THAT said, it's about as well-executed as these things can possibly be. A large, colorful world that's fun to explore, nicely ramping difficulty suitable for younger gamers, an enjoyable absurd sense of humor, and a surprisingly great soundtrack carry the day here.
Spyro is a surprisingly robust little hero with a good control scheme - he can charge enemies, do a diving charge and a "ground pound", blow flames, and roll left and right to dodge using L1 and R1. The main feature of the game, however, is gliding - little Spyro can't fly with his stubby wings, but he can glide a surprisingly long distance after jumping from a high point, and this is very frequently put to use in the level design.
Spyro does initially seem to suffer from what you might call a "lack of challenge" - generous health, enemies that are easy to avoid and dispose of, no "life" system and infinite respawns just prior to whatever segment you died at. The game does ramp up on a slow curve as it goes, though; and the challenge comes more from jumping and gliding segments that become increasingly tricky and more elaborate as the game goes on. It ends up being a fair challenge for adults by the end of the game.
There's an official release for the PSP/PS3 on PSN; if you're hoping to play on PSP be aware that the L2-R2 button functions are missing, and they're pretty key to the experience as they're used to quickly rotate and re-center the camera. With the PSP you're stuck manually repositioning the camera with the analog nub, which sucks. Should be fine on the PS3 though.