I love those kind of games! There are both excellent and less stellar examples, even in AAA games.
The Stanley Parable is a prime example of a game that made excellent use of choices toward reaching multiple endings. The possibility of many actual different endings rather that just variations made this game an outstanding success at this. Though the comical narrator is what really made it so engaging!
On the other hand, Mass Effect made the promise of being a game where your choices would effect your ending, unfortunately it fell short as many of us know. The ending you earned depended primarily on your choices in the last 10 minutes of the game. Your actions of the previous two games, your moral choices, the allies you recruited, your "Paragon" vs. your "Renegade" points, had negligible effect on what ending you could ultimately obtain at the end. The entire series led you to believe that your moral choices would affect the ultimate ending you received and/or your choice of endings. But your ending depended only on what path you chose at the very end: red, green, or blue. This was a huge disappointment for many players. Still it was an excellent space-based RPG that led you to accept that you were really flying through the galaxy trying to solve a great galactic mystery.
Still, it's difficult to make that kind of game because every choice you make that alters the outcome doubles the number of possible endings. To see how this is a problem, do a little math: start with a penny and double it, then double it again, then again, and again. You'll soon see why doubling paths leads to, ahem, difficulty after a few iterations. That's why so many multiple-ending games fall short, or have one ending with just minor variations, or have paths that merge back again after splitting from a prior choice to reduce this problem and have a manageable number of endings. It also seems like a lot of work for a developer to create multiple paths and endings when you know a given player will likely just follow a single path and will never experience most of your game unless they play again and again to experience most of the endings.