When one of your regular players can’t make a session, you have a choice to make: Don’t play, play something else or play as normal.
The first two options are pretty straightforward — let’s explore the third one, playing anyway. When you find yourself in this situation, you can…
Let their PC fade into the background. PCs can be called away, recovering from injuries or simply around but not part of the adventure (although taken to extremes, that last choice is a poor one — think The Gamers). Your group will help you out by suspending their disbelief — just don’t make them suspend it from a crane. This is the simplest approach, and generally the best one overall.
Have another player take over their character. I tried this a few years back, and it worked reasonably well. I got buy-in from my whole group beforehand, and no one ever had a problem with what had happened in their absence. It did, however, require more work from whoever got stuck playing two PCs, and we had to make sure up-to-date character sheets were always on hand.
Play that PC as an NPC. Personally, taking on a full-participation PC role isn’t something I want to do as a GM — but making occasional contributions and ensuring that the PC in question stays out of harm’s way is just fine. Unless there’s a compelling reason to go this route, I generally prefer either of the other two approaches to this one.
When I started writing this post, I expected to wind up with more than three options — but I really think it boils down to these three. What am I forgetting? And which option do you prefer?