No not supposed to.
My current cars are all relatively new - so I would hope not. In the past I've held onto my cars for well over 100k miles, and both over 8 years - no leaking whatsoever. It could be from overtightening of the oil drain plug - that happens alot if you use Jiffy lube type places, it could also just be oil leaking from the valve cover gaskets or oil pan gasket.
It is also possible that it is tranny fluid, but that looks a little different than oil.