I started an IndieGoGo campaign for funding the development of UniPie, a universal pie menu system and on that occasion I decided to collect my thoughts on pie menus.
Convenience is the main reason why I find pie menus useful when it comes to accessing frequently used functions: the pie appears under the cursor so a slight movement of the mouse selects an action. That beats targeting toolbar icons, digging through linear menus or reaching for a key combos.
The use of a pie menu can be greatly enhanced by arranging functions in an intuitive manner, where the movement and the invoked action have some sort of a relation. For example here is a pie menu I hacked together for Adobe Illustrator using AutoHotkey:

The brown slices perform arrangement actions: a small move up or down sends the selected shape forward or backward in the stack while a longer push sends it to either end. The movement of my mouse wielding hand resembles the motion of the selected shape in the stack which makes the learning curve quite shallow.
Or take the blue slice containing file operations: The slice points toward the top left corner where the file menu is located. Executing the “save” action requires less effort since I’ll need that quite often. Export is somewhat related but less often used so it occupies the outside slot. By the way, the blue color comes from the 3.5″ floppy disk which is often used as an icon for saving. The other place where slice color is related to action is Remove Anchor where the red indicates a “dangerous”, destructive function.
Another example for the movement-functionality link could be one of the pie menus I use in modo:

The down motion hides the selection (“I hide it under my desk”) while the up movement unhides everything (“I put things back up onto my desk”).
So with some thought intuitive arrangements can be produced and when muscle memory develops the whole workflow becomes transparent.