Medieval is a bit of a broad topic, so I'll just toss down what comes to mind here. Pretty much all of these could also have fantasy if you want. 

Royalty/Nobles of same or seperate kingdoms. Could be at peace or war.
Knights/soldiers in a war, could be fighting side by side or against eachother, may lead to one being prisoner or a third group being a larger threat.
Royalty or Knight sent on a quest, partners up with an adventurer, mercenary or other such character.
Civilians caught up in whatever mess is going down at the time.
Pair of Hero style character on a quest, or even Hero and Villain.

I have a few more settings more thought out, but that would probably be better put in a pm.