FafnerFafner is the brother of Fasolt, the other giant that built Valhalla for Woton. It was Fafner who complained that the gold alone was not in lieu of Freya because he could still see her behind the wall of treasure. He demands the ring from Woton (who is wearing it at this point). After Woton gives up the ring, Fafner kills his brother and takes it for himself in a possible Cain and Abel allusion.
Woton cannot directly attack Fafner, or else his spear will be broken. Fafner, now in dragon form, is woken by Woton and Alberich, and warned that someone is coming to kill him. Fafner scoffs, and falls back asleep. The next day, Siegfried ends up stabbing Fafner in the heart with Nothung after being led to the cave by Mime. Fafner promptly dies, but not before warning Siegfried about the person who orchestrated the battle.
The Apocalypse Conspiracy* says the following about the Fafner and Fasolt characters, Both brothers are strongly characterized and each one represents a different aspect of the people. The first one would correspond to the utopia of 1789, the one that dreams about justice and about equality. For this idealist, money has no value; only women and love are worth granting efforts. With a lot of common sense he accuses Wotan of sacrificing love and the value of women to sterile stony bulwarks. His brother Fafner would correspond more to the revolutionary of 1791. The ambitions are totally negative.
If he wants to seize Freia [sic], it is only to deprive the Gods of the golden apples, to weaken them, by no means to eat them. He is the one who will urge his brother to agree with the exchange.
ErdaThe goddess of earth and the mother of the three Norns, Erda warns Woton to give up the ring after taking it from Alberich. She apparently has the ability to see the future and possesses great wisdom; on more than one occasion, we see Woton asking for / receiving advice from Erda.
SiegmundSiegmund is the son of Woton, twin brother / lover of Sieglinde, and the father of Siegfried. After running through the forest one night, Siegmund entered the house of Sieglinde and Hunding. Siemund and Sieglinde instantly experienced a strong attraction to each other; despite learning they are twins. Sieglindes husband tells Siegmund that he may stay the night, but in the morning, he will promptly be killed.
Woton, forced by Fricka to defend Hundings marriage rights, destroys Siegmunds sword after Brünnhilde refuses his orders. Siegmund is quickly killed by Hunding (whom is killed by a mere wave of Wotons hand shortly thereafter). However, Siegmund and Sieglinda managed to have one night of passion, which results in the birth of Siegfried.
SieglindeThe wife of Hunding, daughter of Woton, twin sister / lover of Siegmund, and mother of Siegfried. She is saved by Brünnhilde, who hides her near Fafners cave. She took the shattered pieces of Siegmunds sword, which will later be wielded by her son, Siegfried.
BrünnhildeBrünnhilde is the warrior daughter of Woton, and a Valkyrie. She is originally ordered by Woton to defend Siegmund, but is forced to change sides when Fricka reminds Woton that he is required to defend Hundings marriage vows. She defies her fathers orders, and losses her immortality as punishment.
She eventually marries Siegfried, who gives her the ring after killing Fafner with the reconstructed sword. Brünnhildes sister, Waltraute, warns her that their father Woton says the gods are doomed to destruction unless she gives the ring back to the Rhinemaidens, but Brünnhilde's new love for Siegfried is more important to her than concern for the gods. She refuses to give up the ring, and Waltraute rides off in despair.
Siegfried returns to Brünnhilde, transformed by the Tarnhelm into Gunther's form. He tears steals the ring and claims her as Gunther's Bride. Later, at Siegfrieds apparent deception and treachery (she was unaware he was under the power of a magic potion), she reveals Siegfrieds weak spot a spear thrust into his back would be fatal. Hagen, of course, takes advantage of this knowledge and murders him.
When her husband is killed, Brünnhilde considers the gods responsible for Siegfrieds death, regains possession of the ring, and swears it will once again belong to the Rhinemaidens. She puts it on, sets Siegfrieds funeral pyre on fire, and jumps into the flames (but not before she orders her fathers ravens to tell Loge to go Valhalla for the downfall of the gods). The world burns down, the gods are destroyed, and the Rhinemaidens once again posses their gold.
*http://ring.mithec.com/eng/whomime.html - An excellent resource that includes analysis of characters and events.