The only *sim* that I use that doesn't require some sort of controller to get a lot out of it is Train Simulator. It's perfectly controllable with mouse and keyboard. However, if you don't dig trains, it's not going to be for you. I can sit almost anyone in front of FSX or XP with a fast aircraft and a joystick and watch them have fun. But the only person who will sit with me and enjoy watching a train for 30 minutes is my 3-1/2 year old son.
There's one fun racing / crashing / derby sim called Next Car Game:Wreckfest that's a blast to play, and it's actually better with a keyboard than a wheel. It's a stretch to call it a sim though.
Oh, another one comes to mind: Spintires. It's a 4x4 mud / slogging sim, very slow motion, and the vehicles are all sort of Russian and utilitarian. It's more than fine with a mouse and keyboard.
Lots of other *games* I'm currently enjoying without any dedicated controls though.
- Shadowrun: Hong Kong
- Divinity: Original Sin
- Witcher 3
- Endless Legend
- Endless Space
- Dungeons of the Endless
- Invisible, Inc.
- Sunless Sea
- Rocket League (usable with keyboard, better with xbox controller)
I could go on, but that's pretty much my last 6 months of non-sim games there.