Hi there. I wanted to give a shout out to State of Decay, since I think it is not that well known, and I am really enjoying it!
State of Decay is basically an action RPG combined with base management. It's open world, set after a zombie apocalypse out in the American countryside. You just have one save game, and it auto-saves all the time, so it is super tense. I had one of my favorite characters die just now, it was one of those gaming experiences that are great because they are so gutting! There is nothing you can do about it if you screw up.
You switch between a large number of characters with various skills and traits. You can make a team of two and switch between them in the field. Combat is guns, melee and running over zombies in a car. Melee has various special attacks and dodging. If you get more than about four zombies on you, you're in trouble, and there are special zombies that cause big problems (one of them killed my character, I couldn't get away). You have health and stamina, which are hard to replenish (mostly resting at home). Characters can get hurt, tired or sick. There are various guns with different kinds of ammo, and melee items have durability. Cars get smashed up, but can be repaired if your base is upgraded to do that. There's a day-night cycle.
You can go surveying, scout around for items and resources, clear out "infected" buildings, and such at any time. There is also a constant stream of missions basically involving rescuing people, but also trading. Then there are story missions on top of that. There is constant time pressure on rescue missions and also just your base running out of stuff. You have to keep up with the pace or things start to go wrong and someone might end up getting killed. When you look at the map or inventory or base control, etc., the game doesn't pause. You can research and manufacture various stuff.
I haven't finished it yet, but it is one of the best games I have played in ages. It is a budget game, and there is draw-in, clipping, etc. that you have to put up with. So anyway, I recommend it! I'm playing on the 360.