If you recall, one of my primary motivations for giving up on regular campaigns and running an Open Gaming Table was that people kept failing to show up.
It's enormously irritating to come up with some justification for why a character wasn't there one week, when he was there the previous week and the next week. I seem to recall Playing D&D With Porn Stars once came up with a great chart (which I cannot now find) to roll on to determine what your character was doing (and what happened to him) during the session you missed, but that still required sessions to end in town or someplace else where it's convenient for a character to slip out. And if that happens, you can just use the "personal business" handwave. But what happens when you end the session in the middle of a dungeon? Or when one session lasts several weeks of in-game time and the next lasts only a few hours?
So I came up with a new justification, and made it the centerpiece of my campaign. Enter the flux storm.
In the first session, the characters all met on a ship. They were all sailing from various places to the ports of Wang and Endeesy. Suddenly, they sighted what looked like a brilliantly iridescent thunderstorm! The rogue elected to steer the boat straight into the thunderstorm, where it was struck by a bolt of freaky sparkly lightning, which made everyone on board feel all tingly for a few seconds.
Then the half-elf NPC passenger Ned explained that he thought it was what's called a flux storm, and everyone on board was affected by the flux.
What is the flux, you ask? It's basically a time hop effect, except it happens at random, can last any length of time, and you are affected with no saves or checks.
If a player isn't there for a session? Their character vanishes, and reappears next session with no memory of the intervening time.
If a player steps out to use the bathroom or get a drink? Their character vanishes, and reappears when their player returns. (Unless they're in the middle of combat, in which case the character vanishes if vanishing would be harmful for them but fails to vanish if vanishing would be beneficial. If you're about to be hit by the ogre or bleed to death, you can't avoid it by your player ducking out of the room. If you're flanking with the rogue, you vanish if your player ducks out of the room. Leaving the table is sometimes necessary, but to be discouraged. (Do try to take a 5-10 minute break every hour or two, though; human beings can't concentrate on one thing for that long.))
If a player makes a terrible, painfully bad pun? Their character vanishes, and reappears a minute later. (A half-decent alternative to docking people 1 or 10 XP at a time for horrible puns, as long as it's all in good fun. If the response is "I deserved that", you're doing it right. If the response is irritation or outrage, you're doing it wrong.)
If a character dies? A previously-unnoticed character (played by the player whose character just died) who had been on the boat but had been vanished for all the intervening weeks appears.
The basic rule I use, which it took the players a couple sessions to figure out (well, I wound up just telling them), is that you don't just reappear where you vanished: you reappear with whomever you were with when you vanished. So if the party moves on to the next town while you're vanished, you're not left behind or anything.