He's the son of the giant Farbauti and the giantess Laufey, and brother to Helblindi and Byleistr.
Consorts & Children:
He's married to the goddess Sigyn, and through her, he has a son named Nari or Narfi. He also has a mistress, the giantess Angrboda, and it's through her that he fathered the sea serpent Jormungandr, the monstrous wolf Fenrir, and Hel, goddess of the underworld. However, he's also the mother of Sleipnir, Odinn's eight-legged horse, to whom he gave birth after turning into a mare and seducing a stallion.
Notable Stories Involving Him:
Many stories featuring him describe what a sly, crafty trickster he is, with the ability to take many forms (see Consorts and Children above). He's very self-serving, so he can be either good or evil, though he often works against the other gods. In fact, he tricked the blind god Hodr into killing his brother Baldr, then when his daughter Hel agreed to resurrect Baldr on the condition that everyone and everything in the world wept for him, Loki disguised himself as an old woman and refused to weep. As punishment, though, for his role in Baldr's death, the other gods chained him to three boulders using the entrails of his son Narfi, and placed a snake above his head that would drip venom on him. His faithful wife Sigyn holds a bowl to catch the venom, but every so often, she has to empty the bowl, leaving some of the venom to drip on him. In response, he writhes in agony, causing earthquakes. However, when Ragnarok (the end of the world) arrives, he'll break through his bonds, and lead the giants into attacking Asgard, where he and Heimdallr will kill each other.
Loki Around the World:
His equivalents are Coyote the Trickster from Native American mythology, Anansi from African folklore/mythology, and Seth from Egyptian mythology.
SOURCES: Wikipedia, Encyclopedia Mythica, & The Ultimate Online Resource for Norse Mythology and Religion