“ A kingdom where, if there are multiple princes (princesses can't rule unless they have no siblings), the princes fight to the death in the arena to decide who gets to rule. A simple way to make sure your brother cannot make a bid for the thrown, and keeps the royal blood in one line.”
“ The PCs are sent with a diplomat to another country to protect him and do his bidding. There may be some espionage, rescuing, downright bullying, etc. Could make a nice medieval, special operations background.”
“ 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.”