If you play Left 4 Dead often enough then you will stumble into moments where everything just goes excellently for you and you feel amazing when that happens. Same with Wolfenstein: Enemy Territory.
If you're ever that one guy alive at the end of a trial in FFXIV and you win, you feel incredible. Everyone is relying on you, the odds are stacked against you, and sometimes you manage to pull it off.
I remember I once had a game of Halo 3... it was one of those PVP things where you have swords and I am, uh, not very good at Halo 3. And then one day we went in and I basically just had a damned near flawless game (by my standards), topping the charts by some distance. I felt great. I'm not sure I felt like a badass. I was just stunned I did so well considering I'm usually horrible. xD
For single player games... Deus Ex: Human Revolution, I guess? Oh, Batman Arkham Asylum, when you go into that small room with about 50 goons and just beat them all to crap. Uhm... yeah I'm not really sure what else. D:
Bow before the mighty Javoo!
Um, Baldur's Gate II, I guess? I mean, it's hard for me to judge this, but dayum, those high-level abilities!
Honestly, just any game that I play.
My gaming skills are of such a high level that even playing Pony Friends 2 on the Wii makes me feel like a God.
Oh, just remembered another one. Army of Two: The 40th Day has these slow-mo 90's action movie moments where you basically take down an entire army together in dramatic fashion, and you can't help but feel awesome doing it.
Bow before the mighty Javoo!
Any games with cheats or mods. I alway want to be the dominating person in anything I do. My hamster is not allowed to breathe without my permission.
The thing that came immediately to mind for me is Prototype. Not actually the reckless god-tier destruction, but just moving around. It made me feel like such a badass being able to jump around and fly and wall run and all that good trout.
This ties to how good Morrowind feels. Yes, all the big damage wahey is great, but the thing that really makes me feel like a beast is jumping around and levitating and such.
To add to my answer from 2016 Furi and Ghost of Tsushima are games that rely on dexterous skill and make you feel like a badass once you get the the feel and the rhythm of a fight down
Winning some of the crazier fights in God of War 2018 like beating all the Valkyries, you had to be on your A game and it felt great
when certain survival and other gameplay elements aligned just right on Metal Gear Solid: Snake Eater, it really felt like Naked Snake was overcoming some serious struggle and becoming, well, badass. lots of growth and legend-building in that game