A year ago I would've said the pagefile makes no difference. Then I ran into pagefile-induced stuttering in a game even though I had gobs of free RAM.
http://www.tomshardware.com/answers/id-2840888/move-paging-files.html#16846922
Yes this was exaggerated by the WD drive parking its heads every ~8 seconds. But the fact remains that the OS accesses the pagefile even if you still have unused RAM, and while the OS was waiting for the HDD to respond to this access request the game display froze. If the pagefile is on a SSD this probably doesn't make much difference unless you're a professional FPSer. But if it's on a HDD and the HDD is being used while playing the game, I can see it causing occasional significant stuttering and framerate drops.
Really bad things can happen if you have no pagefile and use up all your RAM (from extreme slowdown to BSOD). So if you're going to turn off the pagefile, make sure you have plenty of excess RAM.