I'll second most of Paul's list, especially the Mass Effect, Red Dead Redemption (one of the finest games ever made, from a story point of view even more so than GTA V), GTA V and Saints Row (I need to pick up 4) recommends. Will also add in Burnout Paradise as a trout ton of fun if dated (especially online if Paul has his copy still)

Shooter wise; Halo 4 was a bit disappointing as it isn't bungie made I suppose that and the new enemies feel rather unbalanced. Spartan Ops if you can get past the lag involved is really good fun though. Halo Reach probably has better multiplayer mechanics though although 4 can be an enjoyable experience if you've not played Reach or 3. Speaking of which Halo 3 is free right now with XBL Gold.

Gears of war is a magnificent series and some of the toughest 3rd person game play out there; when me and Psy get our asses handed to us on a plate half way through the 3rd games hardest setting to the point that we've never picked it up to try again (still looking to beat that damn Lambent Berserker boss! whenever you're ready to rage quit some more dude) I'm yet to play the new Gears that prequels the series but I'm not exactly sure I want to tbh, the trailers showed "new weapons and skills" which aren't in the other 3, I get that yes; we need new things to make the game more interesting or appealing but why not provide us a reason for these things not being do-able in games set later in the universal timeline.

Farcry 3 is amazing and expansive, though once you've done most of the side quests to obtain the special weapons and top items it becomes quite routine and linear. I mean sure you can go scavenging for the collectibles (all of which can easily be found by buying maps showing their locations in the world) but realistically it becomes; visit local radio tower, complete outposts, do story missions, rinse and repeat.

Tomb Raider is sitting on my sideboard yet to be played, as is Deus Ex Human revolution

Also; Minecraft! I cannot stress this game enough to you, the hours of fun that can be had just dicking around and not actually doing much of anything is awesome.