This game, the first part of the recent Prince of Persia trilogy, is easily the best of the three. It single-handedly revitalised platform gaming; we wouldn't have Portal if it weren't for PoPSoT.
In terms of gameplay, this game was enormously influential. It fluently combines jump-and-climb puzzles with entertaining combat sequences, more memorable for their visual style than for any real difficulty. Puzzles and combat are shown with great visual flair – graceful character movements, Matrix-style slow-motion, dizzying abysses that occasionally induce feelings of real vertigo. It's all packaged with a compelling and exciting soundtrack. Overall, this is a masterfully executed piece of work, perfectly judged in every respect. In these respects, the game was very influential.
But that's not why it is still remembered, loved, and replayed. At first it seems like an action game; stylish, but ultimately ephemeral; and in fact, that is the most its successors can claim. But the storyline expands, gains shape, and focuses into a simple but beautiful love story. The Prince is a magnificently rounded character: he is gradually chiselled from a hilariously arrogant teenager into a determined and accomplished hero. The heroine helps him, challenges him, and focuses him; his inability to deal with her elicits a witty and charming characterisation of both him and their relationship. The story climaxes, not in difficult action scenes (in fact, in the final battle, difficulty is precisely not the point), but in an act of selflessness that is handled with artless grace and great economy.
This is not an epic, but a novella; not a Doctor Zhivago, but a Casablanca. It is by turns beautiful, charming, heartwarming, and romantic. If by some misfortune you have not played it, please do: if there is ever a canon of games as works of art, this will be guaranteed a place.