I'd recommend...
Grand Theft Auto 4 because it's just amazing on so many levels. Liberty City feels so alive and vibrant, and I am never running out of things to do. In past GTA games, I liked to just run around and screw with the city, treating the game as a big sandbox mode, but GTA 4 just has so much to do that, well... You won't have time to just piss around, even if all you're doing is making taxi runs.
Assassin's Creed is pretty great too. This is what games like Tenchu should have been in terms of assassinating people and the like. The game world is huge (an okay sized town, three sprawling cities and a wilderness map) and a blast to explore. What makes it even better is the fact that if you see something, and I mean anything, chances are you can climb up to it. It's just.. Amazing. This is one of my favourite exploration games ever. I didn't finish the game though, because the actual ingame missions are pretty bland and uninteresting ("Go here, kill guy, return to me.").
Gran Turismo 5 Prologue is fantastic for hardcore racing fans. If you are into arcade racers then you should probably shy away from this, but if you are into racing sims and the like then this is for you. The gameplay is very good, the music and sound effects are top notch. The graphics, however, are simply amazing. Probably the best looking game I've ever played. Just drive the London street course or Eiger Nordwand, a course in the mountains with a stunning view. I have not played the game in SD, and frankly I don't want to. This game, in HD, is quite simply orgasmic.
Honourable mentions to Folklore (action RPG) and Dirt (rally racing) which are both pretty good games too.