It would be quite amusing to say the least.
I think the most interesting thing about it would be that everyone's lives will follow a plot-line of sorts. Bored with work? Get sent to the south China sea on business, and wind up joining a company of pirates. Bored in high-school? School get's attacked by monsters and you end up on a globe-trotting adventure to save the world. Go to bed one night? Have a weird dream, wake up in a new world and have no recollection of your previous life- and then a pair of bloody big angel wings sprout from your back.
It would make conversations at the pub that bit more interesting that's for sure. How on earth it would work for everyone i don't know, the economy would crash unless these adventures only apply to certain people- in which case societies divided between "protagonists" and "background characters".
In general though, things like magic, god's, secret societies, mythical beasts and lots of beautiful big breasted women would exist. Even if i end up as background character, i'm in.