While car seats are not required on airplanes, any airlines in the United States are required to allow FAA-approved car seats to be used if the child has a purchased seat. While lap infants are not guaranteed a seat, airlines will often allow you to install a car seat if there are extra seats on the aircraft. You can check on the side of your car seat to find out if it is FAA-approved.
Booster seats may not be used on board, although the CARES harness is allowed. (Also sold here.)
I like to print out the FAA documentation to have on hand just in case there are any issues!
Here are a few other blog posts on flying with a car seat: Part 1, Part 2, Part 3.
