In the 'Easy question that's actually hard to answer' category we have...
I would have said this question was a no-brainer, but if I'm being honest, it's not that simple to answer after all.
I can name the games I've played most often, in no particular order as to which was played more than another, but picking one as tops is pretty hard.
I play a lot of different games. I modify practically all of them. I kitbash games, and merge parts together. I invent my own. That said, there are a number of games I repeatedly come back to, and run with minimal alterations (see Question #16).
Which was played most is difficult because I might say Star Wars D6 by West End Games, and then a week later run a game of Champions 4E. I hadn't played Ars Magica in forever, then ended up running a game for one group, only to start another campaign with a different group two months later.
The games I've played most in my 40 years in the hobby are (in no particular order - er, besides alphabetically):
Champions, 4th Edition (ICE/Hero Games)
Star Trek, Role Playing Game, TOS and TNG (Last Unicorn Games)
Star Trek, The Role Playing Game (FASA)
Star Wars, The Role Playing Game, Second Edition (West End Games)
Traveller, Classic/MegaTraveller hybrid (Games Design Workshop)
Honorable mention goes to Ars Magica, Mekton I & II, Mutants & Masterminds 2nd and 3rd, Teenagers from Outer Space, and Villains & Vigilantes.
I play a lot of different games.