If you want a stupid fun "kill infinite number of baddies working for an insane BBEG" style game, Just Cause is a blast. 2 and 3 were both fantastic (3 smartly gave you infinite explosives) and the amount of silly chaos you can cause (and are rewarded for causing too!) is brilliant.

For an example, in JC2 there's a mission where you have to destroy a rocket which is launching using a fighter jet and blow up the rocket before it reaches orbit. The ongoing challenge was simply that I'd shoot it until I got too close, not start maneuvering for a second pass until it was too late and instead crash into the rocket dying in a fiery explosion, followed by the rebel leader telling me over the radio that I'd failed and to try again. Then one of the time, I shot the rocket until I got too close, started maneuvering too late, exploded as the plane crashed into the rocket and the rebel leader started saying something over the radio, except it was a congratulatory statement, and I realized I'd instinctively ejected from the plane at impact, and was now falling down to the ground with only my parachute and lots of enemy aircraft trying to kill me. So I grappled to a helicopter, persuaded the crew to let me in (aka beat them up and threw them out) then got shot to hell by another helicopter, which I conveniently would grapple to, persuade its crew to let me in, and keep repeating the process until I finally was close enough to the ground to grapple down to the ground and steal a fast car to evade the enemy army.

JC3 one-ups this by instead of having you blow up a rocket (an ICBM in this case) but instead catch up to and ride the ICBM so you can redirect it to save a major city.