Circlet of Mediocrity: The wearer always rolls a 10 for 20-sided die rolls.
This is an incredibly good item in, say, D&D 3.5. Some prestige classes even have class features that let you "Take 10" on specific skills as significant class features. It keeps you from auto-failing saving throws on a 1, and lets you achieve a 100% success rate with UMD on certain items 9 skill ranks/bonuses earlier than you would normally.
It could also serve as a way to "weigh" dice in gambling scenarios (or if you ran a die-repair/purchase/selling service), although you'd likely be accused of throwing dice in an improper manner if you did so.
Amulet of Heinous Evil: An amulet that, once per day, lets you determine the most Evil (according to your personal moral/ethical standards) action that you can perform within the next 10 minutes (your time, not the Prime Material Plane's time or the amulet's time) and how to get into a position that would allow you to perform said action. The ring calculates the information that it provides its wearer based on the wearer's knowledge, not through a Divination effect, so if its wearer is misinformed or if there are unpredicted factors in play, it could fail to provide the most Evil action available and/or a safe way to be able to execute it, and instead provide an "incorrect" answer. Theoretically useful if you need to prove your worth to a deity of Evil or something.
Ring of Bad Luck: Worsens the wearer's luck and erases the presence of itself from the wearer's mind (even if it is directly looked at, felt, etc.) for as long as it is worn.