Speed cubing is the art/sport of solving Rubik's Cube very quickly, often in competition with other speed cubists. It is tempting to think that a method of few moves would lend itself to speed cubing, however such methods usually require more thinking time. If someone were to train hard enough and lower their thinking time to a small amount, a thinking-based method should clearly beat (by a long way) a memorisation-based method.
My best time to solve Rubik's Cube with this method is 18.95 seconds, and my best average of 10 solves is 28.36 seconds (set on the Rubik's Cube simulator). This is still a way off the world record of 10.48 seconds best and 13.22 seconds average (set by memorisers :-) ).
Some popular methods for solving Rubik's Cube for speed: