Conversation cards have seen use since well before Jane Austen* came on the scene, and they’re still around. You can pick up boxes of cards on different subjects from Table Topics. While not strictly a game, they can easily be turned into one by stealing the mechanics from Balderdash, Wits and Wagers, or Family Feud.

Particularly practical are the versions that come on napkins, which could be useful at a party when you’re sitting with a bunch of strangers.

* Actually, the game called Conversation Cards that Jane Austen played would have been a slightly different party activity: if I’m not mistaken, each player got several cards with words on them and you had to construct a story.