For my current Deadlands game, we've been starting each session with "Story Time". I also used the technique for a Vampire LARP (named Hearts of Darkness, often just called HOD), I ran several years back, and IIRC, the idea of Storytime came from then-Co-GM Dave Hearn.
At the LARP, we had 50 players, and needed a way to convey plot-points more reliably than the grapevine of PCs telling each other what had happened "off camera". So, when a scene was really important, we'd recreate it (or a trimmed-down version of it) for the whole group at the start of the next session. We also used pre-game scenes to foreshadow events, play out the arrival of NPCs, tell backstory and spread rumors. It was a lot of fun, and a very useful tool for our bag of tricks.
We opened Storytime up to players as well, saying anyone who requested it could have 2 minutes of stage and spotlight at the start of any session. We'd usually get about 15 to 40 minutes of material between the GM-prepped stories and the player-performed ones. The stories were for the players, not for their characters - you could use the information gained, but really shouldn't directly reference it in-game.
This being a LARP, sometimes the story-times would end up with some serious production qualities and some real suprises. I remember one time someone told a tale about how their character disposed of a body (torpored vampire, actually), and they brought a bloody (painted, actually) mannequin, complete with stake (painted styrofoam, actually) through the heart. In retrospect, that was awesome, but at the time I nearly wigged out over it, since we were playing in public (college campus) and it looked convincing from a distance.
Then there was this other time when someone else thought it'd be fun to try to do a magic ritual, complete with blood and candle, before the group. I did wig-out that time, and put the player on notice. Never let him do another storytime after that, nearly kicked him out of the game over it.
What I'm doing in the Deadlands game is on a much smaller scale, since there's just 5 players. At the start of each session, I tell one story related to the plot. If players care to tell one, they can do so, and will even get a Bennie (it's like the Tokens in F#) for doing so. My stories are clue-laden, and reveal things relevant to the plot. The players mostly use theirs to develop their characters more. The tales are considered told around the campfire as they travel - they are encouraged and expected to use the information in-character. I wrote a bit more about it a month ago, if you're interested.