I intend run a 6V Dc motor with a 7.4A current rating using a motor driver with an output current of 15Amax. I am told that the motor will utilize the current it requires so it wont be a problem. Do I need to limit the current flowing through to the motor? I know a higher voltage will damage the motor, but will a higher current be damaging?
15A is max. current which can be safely supplied by the driver. However motor rated at 6-7A continuous will draw somewhat more current at the beginning for a short while. Typically this is not a problem with most of motor drivers driving 7A rated motor, but you might want to check data sheet of your driver for the same.
Also in case motor stalls (i.e. motor cannot meet load torque requirements, may happen when motor has more mechanical load than it is designed for.), windings may get damaged if not properly protected.
If the motor is rated to be continuously stalled at a supply voltage of 6 volts then there should be no problem unless the 15 amp power supply becomes damaged due to trying to take too much current (>15 amp).
If the motor isn't rated for a continuous stall then some form of current limiting may be necessary to protect the motor.