2008: This was before my year, but in 2008, 957 used a steering wheel and two beige kit joysticks. The robot had ackermann steering, so the steering wheel controlled the angle of the front wheels. The joystick controlled the left and right drive motors. It did not work very well...
2009: Since we had a crab-drive robot that didn't work very well, I don't recall what we used (it may have had 2 modes, but I'm not sure).
2010 and 2011: Standard tank drive with 2 kit joysticks
T-shirt launcher: Also standard tank drive, but the older beige (pre-2009) kit joysticks
2012 and 2013: Mecanum drive with 2 kit joysticks
Here's the setup we use for mecanum (someone mentioned it in a thread several years ago, but I can't find it):
Linear motion was controlled by the average position of the two joysticks
Rotation was controlled by the difference in the Y axes of the joysticks
In essence, if you move the joysticks "together" (keep them in identical positions), you get only translational motion. If you move one forward and one backwards (as you would when turning a tank drive robot), you cause the robot to turn.
In 2012, I did some testing to compare this setup with using a single 3-axis (four if you count the throttle) joystick, and found that it gives you more control and precision than a single joystick. With a single joystick, it was easy to mix up the lateral and translational axes and there was limited precision in rotational control.