Personally, I'm a huge fan of Sniper Elite on Xbox/PS2/PC. It came out right at the end of the original Xbox's life cycle, around late 2004/early 2005. Basically, you play as an OSS sniper sent into Berlin to stop the Russians from obtaining Nazi nuclear secrets. The story doesn't matter much, it's the gameplay that's awesome.
To the best of my knowledge, it's the first and only game to take bullet drop, wind, body stance, breathing, and other factors into account. So when you snipe a target from long range, you have to really aim carefully. You can even mask the sound of the gunshot by timing it with environmental sounds, like aircraft flying low overhead, or exploding artillery. Really cool game.
Oh, and when you line up a one-hit kill (usually the head), you get a slow-mo, bullet-following camera that ends with a nice, explode-y head shot. Awesome.
It's become somewhat of a cult classic, and I've seen unopened copies going for nearly a hundred bucks. Personally, after I made the poor choice of selling mine in 2005, I recently "downloaded" a new copy for PC. Great game.
