Far Cry 2, but you'll need some patience and a willingness to experiment (also, I recommend the Realism mod since it semi fixes the AI chasing you constantly issues and improves the gunplay).
The later Fallout games are also fun, but you'll want to look up some mods if you want the gunplay to be smoother since Fallout 3 doesn't have iron sights and both titles are rather clunky in combat with the lack of sprinting and giant hit points for everyone.
You also have ARMA II, Operation Flashpoint: Dragon Rising is incredibly "meh", but not outright terrible and its pretty open (though you can't go around exploring the world as you wish without getting yelled at or failing a timed objective).
Borderlands is also very fun, but you should play with friends. Its fun alone, but with friends its a blast. Same for Dead Island (and you don't even get firearms until 1/3 the way through the game).
RAGE is fun, oddly the open world itself is dull and it lacks RPG aspects aside from side missions, but the combat is amazing.
Finally, Deus Ex: Human Revolution. One of my favorite games of 2011, its not really "open world", its hub based but the hubs are completely open for exploration. Much like RAGE, a lot of the combat is interior based, but it does open up more then RAGE in combat (but RAGE also has a pretty open ended combat design, though not on the level of Deus Ex).
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