European Folkloric Beings
The name elf refers to a type of magical creatures associated with woodlands and wild nature. The name is from a very old Scandinavian source, usually rendered as alf or alv.
The stories of the Norse refer to two varieties of elves, both inhabiting the realm of Alfheim: the Liosalfar, or 'light elves,' who were beautiful, sylvan, immortal, and wise; the Svartalfar, or 'dark elves', on the other hand were cave dwellers often connected to legends of the dwarves. These dark elves were unfriendly and often seen as being wicked and cruel.
Norse elves seem to have been as tall as humans, as the name elf travelled across Europe and the British Isles, however, they often became conflated with faeries, pixies, brownies, and other such small, wilderness spirits. As this synthesis took place around Europe and the British Isles, depictions became more variable as regards the size and characteristics of the elves. Often, these elves were portrayed as being quite minuscule (one source refers to them dancing on the tops of mushrooms). These minute beings are frequently shown as possessing butterfly-like antennae and sometimes wings as well. Elves are frequently depicted as possessing pointed ears; pointed or animal-like ears were a common feature in non-human (or bestial/partially animal) creatures, spirits, and monsters throughout the world.
Because of their synthesis with other, similar creatures, the word elf became something of a generic term for small pesky spirits (this is particularly true in late Medieval and Renaissance England, where the word elf seems to have been used for anything small and mischievous—possibly including insects and frogs for all I know!*).
Some elves, such as the Norse light elves, were viewed as being benign but, for the most part, elves were thought to be mischievous—even dangerous. As they were nature spirits, largely representing a culture's views on the natural world, this makes some sense. Up until about the nineteenth century, Europeans (and their American descendants) usually viewed nature as a harsh adversary. With such developments as railroads (to travel farther with fewer hazards), better sanitation, and lighting (to keep people safer at night), nature became increasingly to be seen as a source of beauty and pleasure. The view of elves, first as tricky, often cruel sprites and later as clever, jolly, and beautiful faeries seems to echo these opinions.
Christian thinkers often framed elves as demons or minions of Satan, analogous to imps. The word oaf is derived from the same root as elf, based on the idea that elves sometimes steal human babies and leave changelings (these tales were used to account for children with mental or physical deficits). I have also seen the word ugly connected with their name, for the same reason (supposedly coming from elf-like) but I can not verify that (and there seems to be some evidence to the contrary, so this maybe a discredited etymology).
The idea that elves are the jolly assistants of the Holiday Gift Bringer—merrily singing while making wooden train sets, chuckling warmly over a cup of eggnog, and tending Santa's magical reindeer is very modern, and (I think) in line with our more recent, positive view of elves. The idea of Santa's helpers as a sort of slave labour in green tights, angrily making crummy toys that the fat man could as easily import from China, is sometimes seen in modern humour. I think it probably has more to do with our feelings about labour and industrialization than our thoughts about nature.
Mystical Race from the works of JRR Tolkien
Elves play a large role in the works of JRR Tolkien; they are the oldest children of the creator god. These elves (known as Quendi in their own tongue), are similar to the light elves of Norse myth. They are noble and fair, tall and supernaturally graceful, immortal and immune to the ravages of disease and old age. Tolkien's elves could communicate telepathically with one another.
The elves loved beauty and knowledge and they tended not to associate with other races (such as humans or dwarves) very much, although the wizard Gandalf became a friend to several groups of the elves. Some of the elves were captured by the dark lord Melkor and bred into the vile monsters known as orcs. The elves of Dungeons and Dragons, as well as those of a thousand fantasy novels, owe their existence to Professor Tolkien's work. The bitter and evil elves of Terry Pratchett's novels, on the other hand, owe their existence to Mr. Pratchett's weird sense of humour!
*A joke. I don't really think insects or frogs were called "elves" at any point in history.
References:
Much of this information has been gleaned from a (self-published) book on mythology I have written and am constanly in the process of revising.
Clarke, Kenneth, Civilisation, )British Broadcasting Corporation, 1977).
Foster, Robert, the Complete Guide to Middle-Earth (Del Rey, New York, 1978).
Cavendish, Richard, ed., Man, Myth and Magic, (Marshall Cavendish Corporation, New York, 1970).