There are good answers here already, and they've already hit the key elements of:
- Episodic play
- Re-mixable casting
Any setting in which those requirement can be satisfied would work. However, there is a system specifically designed to support a changing cast and gives something for the characters of absent players to do:
Ars Magica is designed around troupe-style play. Each member of the troupe is intended to GM (called "StoryGuide" or "SG" in AM parlance) sometime, and each member of the troupe has at least 2 PCs - a powerful Magus, and also a Companion, an adventurer comparable to the non-magic users of other fantasy RPGs. The troupe as a whole has a group of serving-class characters called Grogs (a group of grogs is called a turb) who provide muscle and other skills, like smithing and muleskinning. It is expected that for each season's adventure, a different mix of Magi, Companions, and Grogs will participate.
The system also focuses on the long-term research efforts of Magi - so players can say, "Until I say otherwise, if I'm gone, my Magus is studying Rego," and then each session that player's away, you can tick of a season of Rego work for his wizard.
Now, most AM games I have played have "episodes" that take more than one session to complete - but that's just how those stories were designed. A more aggressive approach to scene cutting, etc., in addition to a tighter, more self-contained scenario design could remedy that.