In the original Norse mythology describing Mjölnir's origins, there are no restrictions on who can wield it. Marvel's creation story behind Mjölnir (the first one, not the later "fallen star" background used in the movies) otherwise follows the most popular version of the Norse myth relatively closely.
Mjölnir was the result of a contest between Loki and two dwarves, to see if they could create gifts for Asgard that were better than those the gods already possessed. Loki, of course, tried to cheat by interrupting their work but only succeeded with Mjölnir, causing the handle to be too short to be wielded two-handed. This made it hard for anyone lacking god-like strength to wield it, but otherwise there were no real limitations as to who could wield it. (As a side note - Loki lost, and had his mouth sewn shut as a result.)
In a lot of later Thor myths, he does possess a special belt and gloves - the belt doubles his strength and the gloves permit him to wield Mjölnir one-handed. The three items together are considered Thor's most prized possessions, but they are not restricted to Thor alone. There are several stories of mythological beings such as giants stealing Thor's posessions and Thor having to go get them back.