“ It has been said that within the mountains (or was it the darklands?) there dwells a fluffy creature of immense cuteness. This creature is so adorable that all who encounter it are filled with joy so great their mortal forms cannot contain it. And they explode. Several magic institutions are desperate to study the creature or better yet capture one to prove the theory of an elemental plane of 'D'Awwww'.”
“ The player characters, experienced and somewhat well known, hear rumors and travelers' tales about a distant area being overrun by dragons (or other terrifying monstrosities). The locals have sent them a message, begging for heroic aid.
When they investigate, they discover that nothing of the sort is going on. It turns out that a group of thieves wanted them out of the way so that they could rob them (or someone who would normally receive their protection).”
“ In a crowded marketplace, a man is standing on a soapbox, orating. Some of the crowd are cheering, some hissing, some standing around saying 'I can't hear a bl**dy word he's saying'. It's a hustings for an election. The PCs can either leave, or stay and listen. If they do the latter, then they can vote too, and they might get quite involved in the cheering. Depending on who wins they might get quite involved in the post-election brawl too...
There are numerous possibilities with this encounter: the PCs might end up talking to one of the nervous candidates before their speech, and offer encouragement and support. Of course this candidate may well turn out to be someone with outspokenly unorthodox views, and the crowd don't take kindly to s/his supporters. Or maybe the seemingly innocuous candidate turns out to be a complete racist, and the PCs wander off embarrassedly, pretending they weren't talking to this person five minutes ago.”