Many fly anglers use the same overhead cast on a regular basis, most haul on every cast, some have perfected the double haul for when longer distances are of importance. There are many other additional casts that should be explored by fly fishers based on the fishing conditions and circumstances they encounter where they fish. Casting into the wind, casting weight, tuck casts, slack line casts and more.
Mending should be part of every fly anglers arsenal, using the reach cast it allows you to put slack in your line to get a better float from your dry fly or to let your nymph sink freely. Another cast that is extremely useful is the S cast or serpentine cast. This basically puts some slack in your leader so that you can get a drag free float. It is achieved by wiggling the rod tip horizontally back and forth when delivering the line. On any cast the fly line follows the rod tip so each left wiggle moves that portion of the line left and a each right wiggle moves that portion of the line right and so on. All of these casts and more can be found on the Internet on a variety of sites and can be practiced on the grass in your spare time.