Ring of Snow
A bronze ring set with a faceted aquamarine. The ring can create enough snow to cool a drink or frost to write on a window with the smallest available increment of personal energy (such as Fu in Feng Shui or mental stress in Fate), a packed snowball or frost to cover a window with 2, a 1’ snowball or a slick puddle of ice with 3, and spending an all-day resource (e.g. an AD&D spell level) can make it snow in for several meters around you an hour, or create powder snow in front of you (or ice on water) for 15 minutes (allowing skiing or ice skating), or a big pile of powder snow for soaking up impact. It’s also very handy for keeping cool in hot climates.
This is a teaching tool for magical children to learn to use their internal energy— a sorcerer can even recalibrate it to only work with one particular aspect of it if there are multiple areas of energy to develop. It has very little power, but a lot of style.
Ring of Vengeance
A rose gold ring set with a cabochon white sapphire. By mentally concentrating on a grudge and “pushing” it into the ring, you can store it up so it stays fresh, so you never forget a slight. Once a grudge has been placed there, the associated emotion does not cloud your judgment. The gem turns more and more red as unresolved grudges are placed in it, and clears when the wearer feels satisfied with their revenge. On someone with a long list, it looks like a ruby. Removing the ring causes all of them to show up in a person’s consciousness at once, possibly putting them in a very bad temper.
This is another fun little item that isn’t cursed, but can lead a character down a very dark path.
A gem of blue adamant set in a platinum ring. On speaking the command word, a blade of extremely sharp ice will accrete in the hand bearing the ring, like a snowflake forming in time lapse. (There must be water available to form the blade; in 0% humidity conditions, you could use a flagon of water.) In addition to doing sword damage, it does an extra increment of cold damage as well. The fractal parts of the ice blade break off easily, but new ones form, often out of the blood of the entity attacked; the body of the blade is magically strengthened to avoid shattering in combat. The blade can be quite red after a pitched battle.
Ring of Wishing
Gold ring with a Möbius strip design on the top, the loops of the strip holding matched teardrop-shaped violet garnets. Identification immediately shows you that the ring is connected to a transcendent power of luck, and it grants wishes. As many as you want. (For added fun, put an interesting constraint on this that makes it more believable... once per day, only after having made an offering to a particular power, etc.)
The ring actually causes in the wearer a realistic delusion of the wishes having worked; the further the wishes deviate from reality, the more the wearer goes into a delusional world. The ring can only be removed when they wish that they never made any wishes (or similar sentiments), or they willingly give it away. A paranoid wizard can figure this out with deep analysis, but it takes a lot of digging to figure this out.
Lens of Hatred
A bronze armlet for the bicep set with a large red-orange cabochon carnelian. (If there is a limit on the number of magical rings you can wear, this counts against it.) Focusing hatred and anger into it creates a weapon in the hand of the wearer. The more emotion, the bigger and more dangerous the weapon; someone in a towering rage can create a truly unreasonable creation doing Str+6 damage and looking quite outsize, like a Buster Sword. While the emotions are in weapon form, they do not influence the wearer.
This is in my genre of subtly cursed items, insidious enough that they reward bad behavior instead of directly affecting the characters. In Seas of Chaos, one of the player characters passed it around his order of monks as a teaching tool; if you could summon a weapon at all, you needed to meditate more.