The other driver was at fault for causing a collision and my car is not driveable. Should the other driver's insurance company provide me with a rental car?

Under Ohio law, you are entitled to a rental car if your car is not a total loss and is repairable.  If the cost of repairs is greater than the fair market value of your car, then your car is a total loss.  The law only recognizes your right to a rental vehicle for the period of time your car is being repaired, assuming that the repairs are made quickly after the collision.  If your car is a total loss, the other driver's insurance company is not obligated to provide a rental vehicle, although some will provide one as a courtesy.  If the other driver's insurance company will not provide a rental in this situation, you should check with your own auto insurance to see if you have rental reimbursement coverage that will likely cover this expense.