I wrote a text about dc motors behavior just some minutes ago, here. What destroys a motor is heat generated by current in the winding resistance. As long as you don't load the the motor so that the current stays below the overheating threshold you will be fine. Also, it takes some time for the heat to build up so running a highly loaded motor for very short periods works. Do some test with limited duration and keep track of the temperature by touching the motor and watching out for that characteristic "hot winding smell"
If the motors use brushes for commutation, using a higher voltage will potentially shorten the life of the brushes and/or commutator, due to increased arcing; this becomes especially true for the cheap DC hobby motors that you typically see in these small robot chassis. They usually use a metal strip as a brush (something like nickel or something), which unlike graphite brushes typically arc more.
It should also be noted that the L293, since it is a bipolar transistor (not mosfet) driver, will typically drop around 2 volts (depends on current as well - see the datasheet); so with a 7.2 - 9V battery, expect around 5 - 7 volts at the motor. If you can, shoot for using the high end voltage battery, because the operation will be best if the motor voltage rail is much higher than the 5 volt logic rail.