You probably have heard of (and played) the original "Prince of Persia". It was a megasuccess that was ported to almost every game system in existence, including cell phones and whatnot. This game is a very successful translation of its formula to full 3D, after the very disappointing "Prince of Persia 3D".
This game is adapted for the tastes of modern, more casual gamers, so here a small mistake leading to death doesn't mean you have to replay the whole level. Ubisoft Montreal had the idea to implement a "rewind" feature that allowed to undo failed jumps and stunts so you can try them again instantly. Jordan Mechner, designer of the original game and screenwriter for "Sands of Time", took this idea and ran with it, creating one of the most memorable game experiences ever seen. The story is very well integrated in the game (with cutscenes thankfully kept to a minimum), and your banter with the female interest/sidekick, Farah, makes you care about both characters much more than in most videogames.
The next games were technically better and had some improvements in the formula, but the script wasn't as involving as this one, making this the better game, and for me at least, a classic. This one is the one with the heart, and the game that I keep going back to.