In Super Mario 64, it's possible to get to the top of the castle without using the cannon that opens after collecting 120 stars. Your reward for getting there early?... Nothing! Yoshi doesn't appear until you've collected all the stars! Still, the Wing Cap is there if you've unlocked the red Wing Cap Boxes, and you can't beat the view...
In Sonic the Hedgehog 2, it's possible to collect all seven Chaos Emeralds in the first stage, Emerald Hill Zone. There are a total of seven "checkpoint" goalposts throughout the stage. Pass one with more than 50 rings, and you'll be able to travel to the Special Zone to compete for a Chaos Emerald. Simply repeat the process throughout the entire zone, and you'll be able to play as Super Sonic for the rest of the game!
In Spider-Man: The Movie for PS2, Gamecube and Xbox, there's a glitch in the first Green Goblin fight stage, "Coup de Etat". If you have the "Matrix effects" code turned on, time will slow down for the Goblin when you hit him... But only for him! You'll still be able to move at normal speed! You can hit him, then when he's reacting to the attack in slow motion, run to his side or behind him to score another free hit!