This page is a work in progress.
This is a guide to the many, many untiered rings in Realm of the Mad God, and an attempt at categorizing them in order to help you decide which ring to use on your character. Each ring will be grouped from the more common rings to the rarest.
There are many rings for each class to choose from - As the only equipment slot that every class can use, every ST and UT ring is available for your character to use - as long as you can obtain the thing in the first place, of course.
First up is the Snake Eye Ring. This ring drops from the Snake Pit quite commonly, giving you +3 speed and +3 attack. While this may seem quite low, the Snake Eye Ring also has a reactive proc that gives you 
Speedy for 2 seconds when you use your Ability (cooldown 5 seconds) making this a quite decent swapout for any class without a Speedy effect already.
Next is the Experimental Ring, a good ring for survivablitity, giving 50 HP, 50 MP, 4 Defense and 4 Vitality. Dropping from the Mad Lab, this ring is especially useful for robe classes, giving you extra HP and a decent amount of defense, while increasing your max MP even further for more ability uses. With a max MP stat of 252, this ring could also be useful for a Knight, allowing the user to stun thrice in a short time period if needed, while also giving a decent HP bonus.
The Ring of Pure Wishes is a relatively rare drop from the Candyland Hunting Grounds. It provides 8 defense, the same as the T5 Ring of Exalted Defense as well as 45 max HP and MP. This is another good ring for survivability.
These rings are very powerful and much more rare than the previous ones. Most of them aren’t worth risking on a low-level character unless you know what you’re doing.
The Ring of Decades gives a huge stat bonus of +190 max HP, more than any other ring in the game and 10 more than the T6 Ring of Unbound Health. This ring is tradable, though it is usually very expensive and not obtainable until the endgame. It drops in the Crystal Cavern and Fungal Cavern from the pink Cavern Crystals.
The Omnipotence Ring is a very powerful ring dropping from the Void Entity. This ring boosts HP and MP by 80 each, and every other stat by 4. Any class can benefit from this ring with a decent boost to every stat, but be careful not to put this on an unmaxed character, this ring is a very rare drop.
The Forgotten Crown, dropped from The Forgotten King in the Shatters, gives a hefty bonus of 110 HP, 6 Attack, and 6 Dexterity, making this one of the best rings for DPS while also increasing your max health by a good amount.
Other honorable mentions for UT rings:
Bracer of the Guardian, a good ring, balanced between offense and defense.
Magical Lodestone, another ring with high DPS increase, along with 6 Defense and 6 Speed.
Chancellor’s Cranium, a niche ring with a powerful defensive proc.
Batallion Banner, an endgame ring with a very powerful offensive proc.
Ring of Divine Faith, a low tier ring that gives 5 Vitality and 5 Wisdom.
