There is a disease called "Hand-Arm Vibration Syndrome" which is caused by prolonged exposure to vibration, commonly caused by industrial tools like jackhammers. There are some scientists in London that now believe that videogame controllers that vibrate can cause similar maladies in children.

The key here is prolonged exposure. The case in which this has been an issue was caused by excessive game playing (over seven hours a day) and likely for several weeks at a time. There has only been one reported case of this, in a 15-year-old boy.

There have been no studies that prove that vibrating controllers can cause this problem. In fact, the vibration is so subtle in the controllers, and is hardly turned on constantly, that it would be very hard to prove any kind of link.