The ring in the Viking period was a dominant symbol of fortune, power, and fame. The ring was used as a royal heirloom, a form of currency, and a gift of honor. Much like the Lord of the Rings the magical rings of Viking mythology were also symbols of destiny and symbols of doom.
Andvari's Ring also known as Andvarinaut was a doomed ring which caused much pain in many lives. You can read much more about Andvari's Ring here.
There was another doomed ring known as Thor's Domhring. It was created in front of his temple in a ring of stone statues that surrounded a punishment pillar. It is widely believed that the Domhring symbolized retribution.
There were positive rings created as well. One in which it duplicated itself 8 times in a dripping form every ninth night. The ring belonged to Odin and was called Draupnir. Thor had a ring called the Oath Ring. It was a symbol of fairness and good faith. Many Norse sought it out.
There were also the Rings of Heroes which brought health, wealth, and prosperity unless corrupted by greed. If the wearer was greedy many unfortunate events and sorrow will follow the ring bearer.
The pure rings belonged to Orthnit, Wolfdietrich, and Dietrich. They were symbols of a ring lords circle of everlasting fame and power.
Draupnir Odin's Ring:
Originally crafted by the Dwarfs Sindri and Brokk. Sindri carefully crafted the ring while Brokk pumped the bellows. It was a symbol of infinite wealth and power full of abundance. When Balder later passed away Odin was so heart stricken that he cast his ring upon Balder's funeral pyre. It was later retrieved for Odin by Hermond when he ventured to Hel. This was a great symbol of promise fertility after the winter months.
The Gold Ring:
The ring was extremely well made. It had clear bold lines that express the astonishing handy work of the Viking craft. They symbolized fortune and fame, a precious token of power. They would be buried with the ring bearer to accompany them in the otherworld. It would sometimes be passed down as an heirloom.
Alberich was a dwarf from Niebelungenlied. He formed a ring of power out of Rhinegold that he took without permission from the Rhine Maidens. This provoked the gods and the giants so much so that it forced them into action. The giants Fafner and Fasolt wanted the ring as payment for constructing Valhalla. The grabbed Freyja and kept her until the ring was brought to them. The gods, Frigg, Odin, Freyr, and Thor desperately searched out the ring.
The Ring Andvarinaut was woven with the fortune of gold but held the curse of Andvari. The first to suffer from the curse was Hreidmar. It was given to him from Floki. His son Fafnir filled with lust for gold killed his father. Once Fafnir claimed the ring for himself he was transformed into a monstrous dragon guarding it until his doom when the youthful hero Sigurd slew the dragon. Sigurd took the ring but with it the terrible curse.
After slaying the dragon that was Fafnir, Sigurd inherited the ring. Sigurd was a good man but still suffered from the cursed ring. He fell in love with a Valkyrie named Brynhild. Grimhild used magic to cause Sigurd to marry Gudrun. After the magic faded and he gained his mind back he suffered guilt and deep heartache for what had happened. He was killed by the Nibelung brothers. They were wanted his gold and Brynhild encouraged it to win back her honor. Has the hero Sigurd laid down dying he called out Brynhild name with his last breath.
A Gothic hero known as Dietrich won a fabulous ring from the dwarf Laurin. The dwarf lived in an underground kingdom which he ruled. It was filled with beautiful gems that lit the entire place. After many battles between Dietrich and the dwarf Laurin he overcame the dwarf and claimed the dwarfs magical ring. It contained the power of strength. He also took an invisibility cape, a magical sword, and a vast ring-hoard. Laurins ring was previously owned by Dietrich great-grandfather. the Emporer Wolfdietrich.