In most cases, the rental car agencies keep track of the flight times and know which ones are delayed. You should not have any problems picking up your car a bit later. If you haven't already done so, make sure your flight information is included with the car rental reservation.
Also, if you are at the airport and know your connecting flight is going to be late, you might want to call the company you are renting from and let them know your new pick-up time (especially if it is a holiday weekend where there might be limited availability for cars).