Like Boulder Dash or Magical Drop or Flip n Flop: rapid tap/release motions require speed, accuracy and a specific amount of movement and release response.
PacMan or DigDug or Mr. Do: very precise 4-way directional control. Exceptional precision is required, lest the compass points drift into diagonals and cost you a life.
Fighting games. Lots of accurate quarter- and half-circles. Generally a lot of movement is required, so sticks or larger pads are beneficial.
Shooting games (not the 3D type) like Raiden. Accuracy and release-response are critical. I find a large amount of movement helps: sticks are better than pads.
How about the components:
release response - how fast a controller returns to center
accuracy under pressure - likelihood of undesired input
I welcome your thoughts on the idea.