Loki

Loki belongs fully to neither gods nor giants. Snorri counts him among the Æsir, but his father is the giant Fárbauti and his mother is Laufey, also called Nál. His place among the gods rests on an oath: in Lokasenna he reminds Odin that in the early days the two of them mixed their blood, and that Odin swore never to drink unless Loki was served too. He is Odin's blood-brother, not his brother, and no source makes him Thor's brother; Snorri's list of names for him calls him only a 'kinsman and uncle' of Odin and the Æsir.
Many of the gods' chief treasures exist because of Loki. He cuts off Sif's hair and, to save his skin, gets the dwarves to forge replacements: new golden hair for Sif, the ship Skíðblaðnir and the spear Gungnir from the sons of Ívaldi, then the ring Draupnir, the boar Gullinbursti and the hammer Mjölnir from Brokkr and his brother Eitri (Sindri in some manuscripts). Loki loses his wager with Brokkr, and the dwarf sews his lips shut. Another time he turns himself into a mare to draw the stallion Svaðilfari away from the giant building Asgard's wall, and gives birth to Sleipnir. The gods come out of each crisis he causes richer than before.
With the giantess Angrboða he fathers Fenrir, Jörmungandr and Hel, the three who will help destroy the gods. He puts the mistletoe in the blind Höðr's hand and guides the throw that kills Baldr, and a giantess called Þökk, whom Snorri says people took to be Loki, refuses to weep Baldr out of Hel. The gods bind him with the guts of his own son, Skaði hangs a serpent over his face, and his wife Sigyn catches the venom in a bowl. When she turns away to empty it, the poison falls on him, and his writhing is what people call earthquakes. At Ragnarök he breaks free, and he and Heimdallr kill each other.
Outside the manuscripts he is harder to find. One of the earliest poems to name him is Haustlöng, attributed to Þjóðólfr of Hvinir and traditionally dated to around 900, which tells how he handed the goddess Iðunn to the giant Þjazi and then had to fetch her back. There is no sign he was ever worshipped: no place names, no personal names built on his, no report of offerings. A few Viking-Age carvings are often linked to him, most famously the Snaptun stone from Denmark, a soapstone forge stone with a face whose lips look stitched, which recalls Brokkr's needle. The identification is plausible, not certain. His name is just as hard to pin down.