The PCs find a freshly dug grave, haunted by the ghost of the victim, who will follow them around and wake them at nights wailing "John Smith killed me; avenge my death". They are also hired to hunt down someone who robbed a rich merchant. His name was John Smith. Whatever. Eventually the PCs will go looking for John Smith. He is a local farmer, totally innocuous, who lives on a rather isolated farm near a dangerous area.
When they find him, he tries to zap them with a nasty wand, but after one charge, he drops it and attacks with a sword. He is berserk, but has very few hits and dies rapidly. When they get back to town they are told that while they were gone John Smith left on a boat/caravan/pogo stick. They are confused. They are even more confused when they are attacked by John Smith.
A shape changer/illusionist has got hold of a neat magic item that is supposed to make people believe they are someone else. Unfortunately the item is broken and makes people believe they are one particular person ... namely John Smith, the first person the item was used on. Undeterred, our villain controls numerous people, making them John Smiths and occasionally taking on the John Smith persona to do dirty deeds. Even when there are obviously far too many John Smiths, he'll keep doing this, as people will be reluctant to kill someone who could be their wife, brother or mother!
The PCs will have to tackle numerous John Smiths of varying dangerousness and capture them, determine whether he's a stupid peasant or a high-level evil genius and deal with the situation.
This is great for low-level types without spells that could solve the problem rapidly. High-level PCs would just do a Detection type spells and wrap up.