One haircut in Ásgarðr produced six of the most important objects in Norse mythology, and Sif never gets credit for any of them.
Skáldskaparmál opens the sequence with a single sentence of motive: Loki, out of malice, cut off all of Sif's hair. Thor catches him and would break every bone in his body, and Loki buys his life with a promise — he will get the black-elves to make her hair of gold, and it will grow like real hair.
The commission expands. The sons of Ívaldi make the hair, and throw in the ship Skíðblaðnir and the spear Gungnir. Loki then bets his head that Brokkr and Eitri cannot equal them, and out of that wager come the boar Gullinbursti, the ring Draupnir, and Mjölnir.
So: the hammer that defends the gods, the spear Odin carries, the ring that makes gold, the ship that folds, and the boar that lights the sky all exist because a trickster cut a woman's hair while she slept. Norse myth's entire equipment inventory has one origin, and it is an act of petty vandalism against Sif.
Gold, and grain
Her hair is the only physical detail the sources dwell on, and it produced the standard skaldic kenning: gold is Sifjar haddr, Sif's hair. That is a working poetic formula, used by skalds who needed a way to say "gold" that scanned.
The most popular modern reading takes this further — that golden hair cut and replaced represents the harvest, reaped and regrown, making Sif an earth or grain goddess married to the god who brings the rain. Jacob Grimm proposed it in the nineteenth century and it has been repeated ever since.
It is worth being honest about the status of that idea. No Norse text says Sif has anything to do with crops. There is no harvest ritual attached to her, no place-name, no attested cult, and no myth in which she does anything agricultural. The reading is an inference from a metaphor, and it may well be right, but it is a modern reconstruction rather than a recorded belief — a distinction most retellings quietly drop.
What her name means
Sif is the singular of a noun whose plural, sifjar, means relations by marriage — affinity, in-laws, the bonds created between families by a wedding, as distinct from blood kinship. It is cognate with Old English sibb, which gives modern English sibling and the older sense of "peace" and "kinship" preserved in gossip (originally god-sibb).
So the wife of Thor is named "kinship-by-marriage." Whether that is a goddess whose function is the alliance a marriage creates, or a name that acquired its resonance after the fact, cannot be established. But it fits: the hammer that Loki's prank produced is the same object laid in a bride's lap to consecrate a wedding.
Her family, and a complication
She is Thor's wife. Her daughter Þrúðr, "strength," appears mainly in kenning-lists and in a story about a dwarf named Alvíss who was promised her and lost her by being kept talking until sunrise. Her son by an earlier and unnamed partner is Ullr — which makes the great ski-and-bow god Thor's stepson, a relationship no myth ever mentions again.
Thor's son Magni is not hers; his mother is the giantess Járnsaxa. Móði's mother is unstated. The Norse family tree records this as it stands, without smoothing it.
The accusations
Twice in the Eddic poems Sif is said to have taken a lover.
In Hárbarðsljóð, a disguised Odin taunts Thor by telling him that Sif has a lover at home, and Thor's reply is that Odin is saying whatever will wound him most. In Lokasenna, Sif comes forward with a cup and asks Loki to accept it and leave her alone among the Æsir; he takes it and says she would be, if she had not slept with him — a claim he makes about several goddesses in the same poem.
Both are insults in an insult-contest and neither is corroborated. What they show is that the audience found "Thor's wife and someone else" a usable barb, which may indicate a lost story or may simply be flyting doing what flyting does.
Where she is now
Marvel gave Sif a wholesale reinvention as a black-haired warrior of Asgard, played by Jaimie Alexander, with a fighting role and no marriage to Thor at all — an inversion of the one attribute the sources actually give her. Elsewhere she appears rarely.
The name Siv is in modest live use in Norway and Sweden, and Sif in Iceland — see name histories. For the wider tradition and how thin the record is for many goddesses, see the Norse overview.
Why does Thor not punish Loki more severely for this?
Because the compensation system delivers, which is how these stories usually resolve. Loki offers restitution better than the original loss — hair of real gold that grows — and Thor accepts, exactly as an Icelandic householder would accept a settlement rather than pursue a killing. The corpus is full of Loki causing a specific harm and then producing a superior remedy under duress, and the gods keep accepting the deal, which is why they keep letting him near anything.
Is there any evidence Sif was worshipped?
Effectively none. No place-names are securely formed on her name, no personal names, no amulets, no ritual references. She exists in two flyting insults, one prank narrative, one kenning and a genealogy. That is a thinner record than almost any named goddess in the pantheon, and it is a useful corrective: the tidy modern lists of "Norse gods and their domains" assign her fertility and family and harvest with a confidence the sources do not remotely support.