So in general, you're looking for games similar to what Goosebumps does with some of it's books. Each page takes you to a new outcome or a new event, and then other pages completely end the story there.

Well, in my best guess... the only way to find games like these is to look up that concept online or on bestbuy or some other place that you can find games at.

For example, I'm not entirely sure what game it was for the PS1... but I do recall that this game allowed your characters outcome to change depending on how you played the game. The endings could change between anything from dying to total immortality and beyond that concept.

To be honest, there aren't really a whole lot of games like that... as far as I can come up with, I know PS1 had some games like that, as well as Xbox 360 and PS3 with Skyrim... Minecraft is something like that, although there isn't a definite storyline of any kind.

Uhh, Dragon’s Dogma allows you to control how the story changes throughout the game (Or at least I think it does...), many Mass Effect games allow the story to change depending on the options you pick, and so does Saints Row 3.

Many older games don't, but if you are looking for older games that do... I would suggest looking for PS1 games... that kind of concept didn't really exist back on SNES and Sega (or at least I don't remember if it did).