Since the OP specifically noted that it doesn't have to be a coaster, my favorite launched ride is the steam catapult aboard CVN-71, USS Theodore Roosevelt, "The Big Stick." Zero to between 130-170 mph, depending on your aircraft, in 2 seconds. Hop into a C-2 as a passenger and you "get to" (have to) sit facing backward during the launch.
As long as you aren't the pilot or aircrew, it's an amusement ride as far as I'm concerned.
Second place: probably Kingda Ka.