What to do with that empty seat?

How do you cope with the absence of a player, either in a single session or repeated absences?

My response to this varies, depending on the game — each system and genre can lend itself to different solutions — at least, I’ve employed different solutions, so I want to discuss them.

First and prevailing thought: Most of the people I game with now are adults; people with lives and commitments that can sometimes become very all-consuming. It happens. You have to accept that and work with it. The days (in my opinion) of multi-year-long campaigns, for me, are a thing of the past. Difficult to pull off without player attrition at the best of times, you just can’t go to a typical adult and say “sight unseen, I’d like you to make a weekly commitment to this game for the next two to three years.”
Screw that — 9 times of 10, it doesn’t work. I’ve been lucky about that so far, but I’m done pushing my luck. The games I set up henceforth will be designed as quick jabs, not haymakers: finite arcs that can be played through in 5 to 9 sessions: even on a twice-monthly schedule, that’s only 2.5 to 4.5 months, and much more doable by the typical adult gamer. It also encourages focus on the story and less soap-opera-like meandering all over and squandered sessions where nothing much happens: screw that — get to the next important thing that’s happening RIGHT NOW — we’ll roleplay through an afternoon in a coffeeshop once we’re all independantly wealthy and living in Cancun.
As for playing for four years to get your characters to 20th level? Screw that: if you want to play at all levels of the game, then make up a 1st, 5th, 10th, 15th, and 20th-level version of the character, so we can play whatever we want to play at a given session. Jump around in the time-line… have some fun. (Also, makes it easier for someone to not show up for a session — more episodic.)
Now: setting-specific stuff
Amber:
Nice thing about Amber is that most of the time someone can just be off doing their own thing — the setting lends itself to someone becoming “suddenly unavailable”, even annoyingly so. In the TIHE game, Scott maybe had 50% attendanc emost of the time — PhD candidate in Atmospheric Chemistry — what’re yah gonna do? Lucky, his character was usually off doing stuff anyway, and when he was there, he was totally engaged, which made up for his absence.
Rey and Juli moved to Connecticut for about a year in the middle of that campaign and I just NPC’d them for that period — that worked well enough, I suppose.
D20:
Justin often has to go to bed before the session is over for the night — or he’s been grounded and can’t play that night. Also, sometimes someone can’t make it. In all these cases, we either (a) have someone else at the table play both characters, which is totally a Pawn Stance thing, but whatever, or (b) make up someplace for them to be that isn’t here, which gets easier at higher levels.
The cut-off for attendance is probably 5 people — less than that, and we just call the game and (usually) play something else.
In Star Wars, when Rey dumped his first PC, I just NPC’d them and used them as a plot hook.
Sorcerer:
Small group, intertwined stories, and short story arcs means that if someone can’t play, we just don’t play. It happens.