I think this answer will depend on when you started playing PC games. I'm an old timer. Doom, RoTT, Quake, etc. For me, I've always played most games with the keyboard. I didn't even start using WASD until Half Life came along. The only games I like to play with a controller are racing games.
If however you grew up playing on consoles and you've always used one, then I would think any game would be fine.
We could break it out by game type. There is a reason there are so few RTS games on consoles. You NEED a mouse to play those. FPS again is a toss up to me. I couldn't use one, but I'm sure a PS or Xbox gamer would be fine. Racing games are a must for a controller, or even better an actual wheel. Flight sims are another controller or wheel type game. I have no clue about RPGs, I don't play them.