You will want to look at artifacts, rather than normal magic items.
Most, if not all, official magic items have strictly beneficial effects, or ones that at worst miss/have no effect (like a normal attack or spell).
Artifacts, however, being more powerful, may have negative consequences. (This fits well with your example of the One Ring, which is almost certainly an artifact-rarity item, even if the characters mostly use it as a merely-legendary Ring of Invisibility)
From the Orb of Dragonkind in the DMG:
While attuned to an orb, you can use an action to peer into the orb's depths and speak its command word. You must then make a DC 15 Charisma check. On a successful check, you control the orb for as long as you remain attuned to it. On a failed check, you become charmed by the orb for as long as you remain attuned to it.
And the Hand of Vecna:
Each time you cast a spell from the hand, it casts the suggestion spell on you (save DC 18), demanding that you commit an evil act. The hand might have a specific act in mind or leave it up to you.
Even then, there aren't that many officially-published examples of this, and they are reserved for extremely powerful artifacts.
You make want to look at older editions such as pathfinder as well for inspiration (e.g. Codex of the Infinite Planes) Keep in mind the math for DCs is very different in 3.x systems.