Lord Zardoz said:- Stop the local orc tribe from attacking the village
I did this one with the cliche of "misunderstood"; human barbarians were raiding farms and burning them down - but they weren't killing anyone. It got to the point that the local lord had to ask some adventurers to make it stop.
Adventurers investigate. Only to discover that the tribe's leader, a 14 year old half-orc girl, had been corresponding via mail with the local lord's son. But when she sent a sketch of herself, the lord's son stopped sending letters back. She was crushed her pen pal didn't want her anymore, and wanted him to acknowledge her.
The PCs didn't have to fight them; the party's barbarian/bard wrote a ballad for the girl, about how she was all hot and a prince would sweep her away. She ate it up.
If I wanted to twist it a little further, a third party could have intercepted the correspondence, in order to push the conflict.