Everyone in the Portal universe.
Everyone in the Metal Gear Solid series. (At least Twin Snakes and Snake Eater)
Everyone from Donkey Kong Country (omitting Candy)
Now for specifics, with their specified appearance:
TipTup the Turtle (Diddy Kong Racing)
Link (Ocarina of Time)
Doctor Mario (Super Smash Bros Melee)
Yoshi (in any third-party Mario title such as Kart, Party, etc.)
and that's all I can think of for now.
I know the OP says no Rare games, but I had others. So suck it.