Fly Casts by Category/Purpose
The following is a list of fly casts categorized by their primary purpose. At the bottom of each description are several links I find to be especially well done with highly qualified instructors and good quality production.
I believe, as do many others, that the roll cast is the second most important cast to learn. The roll cast can be used in many situations. Off the top of my head (1) when there is no room behind you for a backcast (2) when the wind is coming from your back and interferes with your backcast (3) the roll cast can be very useful in getting your fly line in the air quicker to begin another cast because you do not have to strip the line in as much as would otherwise be the case.
This is the most basic cast in fly fishing and virtually all other types of fly casts are based on the overhead cast. It is the first cast that is taught to beginners and it is the one used a great majority of the time by fly fishers. It is also one of the simplest casts. As I have said, the importance of really knowing and being able to reliably make this cast time after time is the key not only to your success as a fly fisher but it is also the foundation of many of the "specialty" casts you will want to learn.