I've done this twice, and it was really amazing both times.

One was a Victorian era game, and all the players started out in unlocked jail cells, with the guards lying on the ground dead. A mob of townsfolk was outside the jail, trying to lynch them. All the PCs were in the town because they were after the same guy (each one had a different reason for wanting to find them, none of them really wanted to let him live), but none of them could remember how they got there. Every day they would wake up the same, and they would try to do something about the guy. However, things changed each time (not just because they do something different, either). After a few days of noticing these "errors", they started having flashes of something else entirely while they slept. In the end, they were all in a mental "hospital" being put through a sort of shared recurring nightmare.

Another game was set in a traditional medieval fantasy world, and they all started as peasants. There is an oppressive guard force in the town, and an incident happens that causes it to escalate into a massacre of the town people. They would wake up each morning with knowledge (and xp) from the previous day, but it would be the same day. They were able to use their prior knowledge (and new abilities) to change the course of events. They eventually found that the problem wasn't just local, and they worked their way to the capital, where they found that two powerful wizards were battling it out for the fate of mankind. The good wizard "lost", but managed to maintain a spell that would allow the PCs to be outside a time loop, allowing them to gain the power they needed to stop the bad guy. The every time the day was repeated, though, the villain pushed against the wizards effect, and when the PCs finally get there, he breaks it, and kills the good wizard. The PCs, now higher level, had to fight the evil wizard without the benefit of being able to "try again" like they had been. The last few sessions were super tense, as they understood that if they died, there was no coming back (something that hadn't been true before.