Wagner's Ring Cycle is about a curse on a ring, but in another (even larger) sense it's about a curse on women. Four women in the four operas are forced to marry and submit to a man against their will.
The first we encounter is Freia, who is Wotan's sister-in-law. Wotan contracts with two giants to build Valhalla, and he agrees that if he is unable to pay he will give them Freia. He never had a way to pay them, so when they demand their money he gives them Freia (to the horror of Freia and her siblings) - but then discovers that the gods will lose their immortality without her, so he steals the Rhine gold to give the giants instead.
In the next opera we encounter Siegmund, who is pursued after trying to free a woman who is being forced into marriage by her brothers. Siegmund seeks refuge in a house, only to discover that his twin sister Sieglinde lives there - they were separated years before when bandits abducted her and forced her into marriage with the cruel Hunding.
Next up is Brunnhilde herself. Daughter of the earth goddess Erda and the sky god Wotan, she is the head of the warrior clan the Walkures. A virgin goddess, no mortal man can meet her gaze and live. But she disobeys Wotan and in punishment he turns her into a mortal, leaving her helpless on a mountain to become the slave of the first man who finds her. She thinks she has broken the curse by convincing Wotan to surround her sleeping form with fire so that only the greatest hero will be able to win her - and that plan seems to work until her hero, Siegfried, is drugged and duped into forcing her to marry another man.
Other characters suffer minor versions of the this sexual predation. Fricka is humiliated by her philandering husband Wotan. Erda is duped by Wotan into giving up wisdom, and after bearing Brunnhilde for him she loses much of her power. (Even one male character, Siegfried, is given a drug that makes him forget his wife Brunnhilde and think he loves Gutrune. But you have to feel that Siegfried is partly to blame: why did he leave Brunnhilde so soon after finding her? Why did he trust his hosts so stupidly?)
There is nothing subtle about Wagner's theme that women are not free in love - the repetition and drama smash us over the head with it. In a piece of art that is so preoccupied with the idea of love, this is a heavy undercurrent of darkness and cynicism.
(Love is not all rosy in other ways, either. Alberich is able to steal the Rhine gold only after he renounces love - but he does that after some pretty cruel taunting. The two great romances in the cycle are both incestuous: Siegmund with his twin sister Sieglinde, and Brunnhilde with her nephew Siegfried. There is much passionate love-making, but all of it is creepy.)
Erda, the earth goddess, has a relationship with Wotan off-stage, between the first and second operas. All we know is that he wooed her to obtain her wisdom, and then Brunhilde was born. Erda goes into a steady decline after that, sleeping almost all the time. When Wotan cut a branch of the World Ash tree to use as his staff of power, the tree slowly withered and died; the same seems to happen to Erda: this appears to be a zero-sum game, where power gained by one player causes another to lose it.
The only married female character who is not in an unwanted sexual relationship is Fricka, Wotan's wife. Fricka is the goddess of marriage and her major motivation in the text is to find ways to keep her husband from dallying with other women. (She is not successful.)
There are other female characters in the Ring Cycle. The Walkures are virgin goddesses, depicted as proud and free (although they exist to serve Wotan by collecting heroes who die in battle to serve in Wotan's army). The Norns, daughters of Erda, don't appear to have lives outside of their job of untangling the ropes of fate. The Rhine maidens, mermaids who guard the Rhine gold, are definitely sexual beings, but it is not clear that they do more than flirt. Finally there is Gutrune, spinster, who drugs Siegfried to make him love her, but her actions are manipulated by Hagen, who is scheming to get the ring.