Games Like Far Cry 3/4

Ghost Recon WIldlands, Far Cry 3's Blood Dragon, Borderlands, Fallout 4, Just Cause 3(if you do not mind the third person camera), and Crysis.

Metal Gear Solid V, maybe.

Postal 2
http://store.steampowered.com/app/223470/

Cheap, fun, a bit crazy, and classic
(No driving or open world though, only in town)

I cant speak to how good the game is but you might want to look at homefront revolution, its an openworld fps where you are in a resistance fighting the big bad military group.

Skyrim? It's basically Far Cry 3 without guns.

More serious now: Skyrim probably would fit that bill, Saint's row IV or maybe Dead Island/Dying Light too. Could always try Far Cry Primal too.

STALKER series maybe? Similar in some ways, but very different in others.

Oh man I love Far Cry 3. Still haven't played Far Cry 4 - too expensive for me. :P

I'd recommend Far Cry 3: Blood Dragon, if you have haven't played it yet. Basically a reskinned, slightly ridiculous Far Cry 3. It's a bit short and lacking in content for a standalone in my opinion, but it's a nice little addition to the far Cry franchise which revisits the same base gameplay but with a few slight adjustments which makes the game quite entertaining to play.

What about the other games in the series.

ghost recon wildlands is your best bet.

dying light / the following

You'l love The Sabouter. Otherwise try Red Faction Guerrilla, Saints Row 2, Saints Row The Third, nothing else comes to mind that would match your mentioned preferences.

Far Cry 2 or FC3: Blood Dragon

How about the Crysis series?

Saints Row 3 fits that description. Saints Row 2 and 4 also probably do but I haven't played them.

I think a lot of ubisoft games are similar so try checking out their other titles.

I'm gonna say that the Far Cry and Just Cause series are very similar, so go there. If you want to branch out, Saints Row and GTA are fairly similar to each other. They're probably the next ones you should try. Skyrim/Fallout series have much stronger RPG elements, but are a nice diversion. Ghost Recon / Homefront revolution are more tactical. Dead Island... well, do you like zombies?

The rest of what's mentioned so far, either I'm not familiar with, or I think are too dissimilar to be worth mentioning

Far Cry 2

As mentioned by others, you can always play the older Far Cry titles, both of which are good. The biggest flaws are that in Far Cry 1, if you barely rustle a bush, mercs with handguns can (apparently) shoot you in the head from 500 yards away, so it has some balancing issues. Far Cry 2 fared better, but is pretty grindy, especially with regard to the quickly respawning mini-bases that are constantly in your way in the road. So, neither of these are as good as Far Cry 3, but they're still both worth your time, especially because you can probably get them really cheaply.

I'd recommend FC3 Blood Dragon as mentioned above, too. It truly is ridiculous, but that's kind of what makes it work. It has more focus on the FPS part and less on the RPG part (which is greatly simplified), and that's a good thing for what they're trying to do. The moves are SO awesome because they're supposed to be cheesy 80s sci-fi action movie stunts, and the hilarity works. I may have even enjoyed the gameplay more than regular FC3, even though it doesn't have the same level of depth.

Someone mentioned the Stalker series earlier...I liked those a lot, too, although there is a lot heavier RPG element to those. But, very good games. Well, I might avoid Clear Sky...it's shy on plot and strong on frustration, but the other two games were great. The Metro series was good too, but it's a little more on-rails and less open world.

Deus Ex? Not completely open world, but lots of choices as to how you want to approach it, and what order you'd like to do things.

Far Cry 1+2, though 2 can get annoying. The Saboteur, Red Faction series, RAGE.

I know it's old but Just Cause 2

Tomb Raider obviously. Just Cause 3 doesn't have a storyline, so avoid it. Mafia III too. Watch_Dogs 2 maybe too? But Tomb Raider is mostly the one related to it.