In Norse mythology, Loki is known as a trickster. He is described in the Prose Edda as a "contriver of fraud". Although he doesn’t appear often in the Eddas, he is generally described as a member of the family of Odin. Despite his divine or demi-god status, there's little evidence to show that Loki had a following of worshippers of his own; in other words, his job was mostly to make trouble for other gods, men, and the rest of the world.
A shapeshifter who could appear as any animal, or as a person of either sex, Loki was constantly meddling in the affairs of others, mostly for his own amusement. Disguised as a woman, Loki fools Frigga into telling him about the weakness of her son Baldur. Just for fun, Loki tricks Baldur's blind twin, Hod, into killing him with a spear made of mistletoe. At one point, Loki spent eight years disguised as a milkmaid, and got stuck milking cows because his disguise was so convincing.
Loki is typically described as the husband of the goddess Sigyn, but he seems to have procreated with just about anyone and anything that struck his fancy. Because he could take male or female form, at one point Loki turned himself into a mare and mated with a mighty stallion, so he actually was the mother of Odin's magical eight-legged horse Sleipnir.
Loki is known for bringing about chaos and discord, but by challenging the gods, he also brings about change. Without Loki's influence, the gods may become complacent, so Loki does actually serve a worthwhile purpose, much as Coyote does in the Native American tales, or Anansi the spider in African lore.
There is little archaeological reference to Loki, but in the small village of Kirkby Stephen, England, there is a tenth-century stone with a carving on it. It is believed that the bound, horned figure carved upon the stone is in fact Loki, who was likely brought to England by Saxon settlers in the area. Also, near Snaptun, Denmark, there is a stone from around the same time as the Kirkby Stephen stone; the carving on this one is identified as Loki as well, due to scarring on the lips. In a story in which he tries to get the better of the dwarf Brokkr, Loki is disfigured and earns the nickname Scar-lip.
For an excellent dissertation looking at Loki in his many forms, read Shawn Christopher Krause-Loner's paper Scar-lip, Sky-walker, and Mischief-Monger: The Norse God Loki as Trickster.
Loki has seen a resurgence in interest lately, due in no small part to his portrayal by actor Tom Hiddleston in movies such as The Avengers.