Clutch woes, burning the discs?

My family has three cars - a 2003 Civic EX, a 1989 CRX Si, and a 1985
Corolla SR5 - that are all 5 speeds. However, the clutches aren't
lasting very long in any of them. They give identical symptoms, a
vibration or shimmy as the clutch plate is grabbing. Once the clutch is
engaged, its fine and does not slip. My question is, what might be
causing this? A particular style of driving? Is the plate being burned
(a mechanic has told me this before) or is another part failing?
Thanks!