Farragomate is the social, webby version of that very same pastime.
You get to play with a bunch of random strangers in real-time, and make up sentences out of a pre-set collection of words, including some fairly naughty ones, and all players' nicknames. As you can imagine, some of the results are not child-friendly.
There are ten rounds to a game. Once a round is done, players get to vote for their favorite sentence from that round. You can't vote for your own creation, of course. There's in-game chat, too.
I think the vocabulary could be made a bit more eclectic, but even as it is, it's a nice way to spend a few minutes and meet random strangers on the Internet (always a thrilling experience).