The only game type I can think of that lends itself better with a controller then a mouse and keyboard for me would be fighting games like Soul Caliber etc. Everything else I tend to use a mouse and keyboard for, even games I used to use controllers for like platformers or racing games.

I much prefer using a 360 wireless controller, even for FPS games on my PC.

I have large hands & I find that in a game which has lots of other command buttons, like Crysis, I tend to mash other keys in the heat of battle & sometimes unwittingly exit to Windows or do something else undesirable. I couldn't even get into Crysis until I played it with my 360 controller, I found changing the suit modes at the same time as running, jumping & crouching too awkward on the keyboard.

Also, due to the nature of my PC set-up & furniture (my desk is about 1.5 feet higher than my armchair & about 3.5 feet away, & it doesn't have a lot of space on it), using a mouse & keyboard for a long period of time results in a sore shoulder & other RSI's caused by bad posture.
Also my keyboard can fall off my lap in the heat of the moment, leading to disaster if the batteries pop out on impact.

I know that the mouse&keyboard is supposed to be more accurate than a controller for FPS games, but I'm not competitive enough to sacrifice the comfort & freedom my wireless controller give me. For instance I can't stretch out in my armchair & play with my mouse & keyboard behind my head like I can with the controller.

Obviously this doesn't apply to RTS games & games like Civilisation, but those don't have the same pace as FPS games so don't warrant having all you controls immediately available in your hands.

I really only use a controller for action games, platformers or sport games. Everything else is just better with a mouse/keyboard

It's different for different games.
Mouse and keyboard for FPS though.