Any time a quest giver gives you a quest that isn't finished.
I just tested it in classic. There's a simple way to show it:
1. Enter a Fighters Guild, without the 24/7 rank benefit.
2. Rest until midnight.
3. Either accept a quest or don't.
4. Save the game in front of the questgiver.
If you load the game with a quest active, the QG will be there but no one else.
If you load the game without a quest active, no one will be there.