I think your Sonic 3 example is a good one. And no, you're not the only one who got held up at that point. Me, and all my friends, always had trouble with it too.
Well, I could spout the names of several different adventure games and call it a day (Riven, in particular, jumps out at me), but I've got another good one.
In one of the X-Men games for the Genesis (I forget exactly which one it is at the moment), when you get to the end of the game, you basically reach a dead end, with no way to proceed. The solution? Hit the reset button on your console. THAT will take you to the final screen.
What in the flying name of FUCK would lead you be believe that would work?