Rainbow Six Vegas. This is actually one of the very first games I ever got on the 360, but it is fantastic! you should also get Vegas 2. They're both great, but I prefer the locations and maps of the first one a bit more, although some are in both. They should both be very cheap now anyway. T Hunt is very fun as well!

Call of Duty. Maybe you're not into these games anymore, but if you're not, I still recommend you check out Call of Duty 2, 3 and 4. They're all fun to play anyway, so maybe just consider getting the whole series after a while. Keep in mind though, the multiplayer on MW3 is strange. The maps aren't that good (they're alright), and the game feels un balanced because of spawn and weapon issues. You can still find the perfect balance though and there are a few of the maps which are pretty good. Not the first CoD to recommend to you though if you haven't got any. I would start with CoD2 or 3, they're the best on the 360 anyway, in my opinion. 4 is pretty good as well.

GTAIV and Episodes from Liberty City. The single player stories may not seem as interesting as the old GTA games, but they are still pretty good. These games are all about the online free roam for me anyway. Great fun and spent many hours playing on it!

Saints Row series (1, 2 and The Third). These are great games as well. The first is nowhere near as good as 2 and 3 in my opinion, but it's still decent and it finishes the collection. It should also be really cheap now anyway. The best are 2 and The Third. The Third came out last year. But wait! there is a version called The Full Package (Saints Row The Third) coming out in a few weeks which includes all three of the DLC stories for The Third (and the main game), and some other random DLC such as clothes and stuff, so if you are looking in to getting it, you should get that one. It is also not a full price release as far as I am concerned. I could say more games, but that's enough for now :P.

Gears 3, what an amazing campaign, trying to beat it again on insane. Gears one was absolutely amazing for its time. Gears 2, was so hit and miss. The improvements and new weapons and enemies were fantastic additions to the series, but the glitches and sub par story kinda hindered it. Also the MP was a mess.GhettoBlastin92

There's a few that come to mind that creeped me out the most

The Regenerators from RE4, Mr. X from RE2, Nemesis from RE3 and the Chainsaw guys from RE4. The Chainsaw guys and the Regenerators may not seem that bad, but they are. The Regenerators can well, regenerate and you always know that if you don't sort the Chainsaw guys out they will be after you as you're running away :lol:. They're pretty creepy.

The worst though is either Nemesis or Mr. X. It's actually a tough choice. Mr. X may be slow and Nemesis may be VERY fast in comparison, but Mr. X CORNERS you and he can climb and stuff... yeah, it's a tough choice between those two :P.

The Tomb Raider series could be great for this! not only does it make you think, but it's not stressful (besides the times you jump out of your seat when a piece of the awesome soundtrack comes on when an enemy attacks along with it, or when an enemy attacks alone :P). Those are mainly the old Tomb Raider games, but the new ones are still good and still can provide you with a relaxing time in the way that it not be frustrating (unless you get REALLY stuck :P but that's what makes it good). Of the new ones, I recommend Anniversary (remake of TR1). Best TR game of this generation I think. Not as good as the original, but none of them have beaten the originals in my opinion.

I would also recommend the Rock Band and Guitar Hero series if you have never played them. When you get decent enough at them, you can just sit back and have fun on them.

Well as for the Xbox, it would definately be the Gears of War series :D. That is always the first one that comes in to my head... one of my favourite series.

To be honest, I can't really think of anything else. But Gears of War is a series that you should definately play, if for some reason you still haven't :P.

The only other big exclusives I can think of are Forza and Halo. Forza is a pretty good Racing series and Halo is an average FPS series in my opinion.