The amount of current drawn by the motor depends simply on the amount of torque that the motor is producing, so when it is unloaded and up to speed the current with a 9V supply will be the same as with a 3V supply. However, at the other end of the scale when the motor is stalled the 9V supply will put up to about three times more current and up to about nine times more heat into the motor. Obviously that would have a drastic effect on the life expectancy of the motor. If you kept a small motor stalled and powered up at three times the rated voltage, you could probably burn it out within a few seconds.
Tripling the supply voltage would triple the free-running speed when the motor was unloaded. The effect of the increased RPM would depend on the quality of the motor. A really cheap motor might start shifting and flexing to the extent that went out of balance and was destroyed.
Basically, this isn't something you would want to do to a motor that you wanted to last.