Just Cause 2 is the absolute best game for this ever.
It's shooty, yeah. But it lets you do things like lure an enemy patrol truck to an airport, then attach their truck to a departing airplane with your grappling hook. Also, what other shooters let you pick up machine gun emplacements and haul them around, complete with infinite ammo?
You also get to blow up all the things.
If you enjoyed GTA but wanted more, this is the way to go. If you just want to feel like a freaking awesome guy doing freaking awesome things without any reason or motivation beyond freaking awesome, you can't beat Just Cause 2. There's no more awesome feeling than flying high into the air, seeing a random plane, skydiving into its path, grappling onto it, taking it over, crashing it into whatever object you feel appropriate, and then using the grappling hook with your parachute to escape the angry natives. The plot is Grade A Dumb, but, in spite of that, some of the missions are pretty fun.
Did I mention there's a giant island to explore, with thousands of things to blow up?
This, so damn much. Just Cause 2 is and always will be my go-to for absolutely pointless, destructive fun. It somehow managed to create the perfect storm, like a living action movie, except it lasts for dozens of hours and the plot can be ignored entirely.
Plus, your best mode of transportation is to repeatly grapple towards the horizon, briefly open your parachute, grapple again, etc. You can get up to absolutely absurd speeds and climb up vertical cliffs. Seriously, it's like you are some sort of mix of Spiderman, James Bond, and Bruce Willis. I once spent four hours attaching cars to commercial airliners as they were taking off, hopping inside, and climbing out onto the roof at cruising altitude. As mentioned, you could steal military jets and ghostride. One of the missions had you steal a jet so that you could shoot down a bloody ICBM. When you are being chased by enemy vehicles, you can climb onto the roof of your own, use your grapple to connect two of them, and watch as they crash into each other. Some of the best fun I had was sneaking into military bases with colonels, planting demopacks on as many target buildings as possible, sneaking onto a roof, sniping the colonel, then detonating everything and running away. I really could gush for hours about how perfectly executed this style of freeform destruction was.