Unfortunately you'll come across it soon enough if you'd played any games for any length of time: Bad controls. I've played a few myself.
Among these are:

Beyond Two Souls: The controls for Jodie are great. For Aiden not so much. It's nearly impossible to move where you want.
Sonic Unleashed for the Wii: Movement with just the remote is impossible and movement with the numchuck and remote is even worse.
Heavy Rain: The characters are nearly impossible to control, and the on screen prompts for certain buttons says you did it wrong when you did exactly what it said to do.
Grand Theft Auto IV: The driving and moving is fine, the fighting is not. The character's punches and kicks are extremely slow or don't hit at all so you end up getting killed.

What are some games that you've played with bad controls?

Final Fantasy 13 - controls are confusing. 'nuff said.

I bought the Mirror's Edge PC port for $5 a while back even though I already had it on the 360 and the controls did not translate well to a keyboard at all. I have to play it with my 360 controller plugged in. Otherwise it's actually a pretty decent port. The graphics are upgraded from the shitty 360 ones and some of the lower res textures that seem to have been completely replaced.

Kirby Air Ride for GameCube. Omg they make you use the A button AND the control stick. If it don't use 1 then I ain't buyin 1.

Dark Souls PC... I don't have a controller so I can't play at all

Zelda: Skyward Sword. It has the worst controls in any game I've ever played.

So I recently bought Sleeping Dogs Definitive Edition and the game is impossible to play without a controller.

Sleeping Dogs Definitive Edition can be played without controller only the thing is it needs lot of practice.

Some older gamed were pretty bad in that department. E.g., Gothic was a great game but controls were quite a chore to learn - nothing was where it should be.

The Witcher, horrible clucky combat controls. Witcher 2 was better, but could still be improved, the first half of the game is dodge dodge roll roll hit dodge dodge roll roll hit etc.
Let's hope Witcher 3 is going to be better.