In Denmark the elves seem to have merged with the Huldra and are beautiful females who can dance a man to death. If you see them from the back, they are hollow.
In Scandinavian folklore, which is a later blend of Norse mythology and elements of Christian mythology, there are several groups of human-like nature spirits than are akin to "elves" in a modern sense. These are called tomtar, vittror, and lvor, and are grouped under the general name of vttar (compare wights).
The Brothers Grimm fairy tale The Shoemaker & the Elves is probably the most famous original elf tale. The elves are only one foot tall in this story, naked, and like to work on shoes, as leprechauns do. When the shoemaker rewards their work with little clothes, the elves are so delighted, that they run away and are never seen again. (This tales is echoed in J. K. Rowling's Harry Potter stories: see below.)
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Tolkien is responsible for reviving the older and less-used terms elves, elven, and elvish rather than Edmund Spenser's invented elfs, elfin, and elfish. He probably preferred the word elf over fairy because elf is of Anglo-Saxon origin while fairy entered English from French.