What are some of the most popular game times today as well as historically.
Blitz games will have 1-5 minutes per side.
Most tournaments will have 1-3 hours per side. A popular setup is 1-2 hours per side for the first 40 moves, plus an additional ½-1 hours each after the 40th move. They may also allow Bronstein/Fischer time, if the clock supports it.
The official FIDE time settings are 90 minutes for the first 40 moves + 30 minutes after move 40 + 30 seconds for every move.
The last world championship was "120 minutes, with 60 minutes added after move 40, 15 minutes added after move 60, and 30 additional seconds per move starting from move 61."
Fast time controls are more current these days. You can find a lot of 30/30 (each player has 30 moves to make in 30 minutes) and G/30 (each player has 30 minutes to make all of his moves) in over the board tournaments. Slow time controls are still out there, but with the rise of Internet chess, even over the board tournaments are going with quicker time controls. On the Internet clubs you can find blitz chess (usually something between 3 and 15 minutes for each player to make all of his moves) and bullet chess (under 3 minutes for each player to make all of his moves); although the Internet allows for slow chess too, it may take a while of waiting, and good deal of patience, to get a game.