Prince of Persia: The Sands of Time completely changed my life. The story is so GOOD, the gameplay is just challenging enough to not piss off previous generation gamers, and just easy enough to not make next-gen n00bs cry. It is... the best game I have ever played in my life.
Plus, it introduced me to the wall-run. And back then, I used to think with the logic that it's in the game, and someone must have thought of that. If someone must have thought of that, then it exists in some form in real life. One Google search later and my life was changed forever because of:
The discovery of Parkour.
PoP pwns.
I have vowed to buy every single PoP game that is an action-adventure.