(here are some helpful descriptions of the rings in zOMG)
Melee Attacks
Bump

Turn that hip around and BUMP your opponent away from you. Knocking them FAR away at higher Rage Ranks. The process *is* painful to your target.
Dervish

Whirling at incredible speed, you deal damage to all foes close to you. Higher Rage Ranks knock your enemies farther back and increase the area you hit.
Hack

Land a colossal blow to your foes! Hits things hard, even causing them to bleed for a bit after you hit them. At higher Rage Ranks, the bleeding lasts longer, thus causing more damage.
Mantis

You create a katana from nothing to do your bidding. Does light damage, but attacks again very quickly. At higher Rage Ranks, it also drains an enemy's Willpower.
Slash

You slash at the nearby foes in front of you, doing damage to all that you hit. Your slash becomes wider and deeper at higher Rage Ranks, allowing you to hit more enemies.
Ranged Attacks
Fire Rain

Summon burning rain from the sky to fall in an area around yourself damaging your foes and draining their Willpower. Higher Rage Ranks result in bigger damage areas and greater Willpower drains.
Guns, Guns, Guns

When all else fails, haul out the artillery and drown your target in lead! Higher Rage Ranks create a wider spray of bullets, causing more damage in a bigger and bigger area around your target.
Heavy Water Balloon

You create a giant water balloon and hurl it at your foes, causing a colossal splash in a large area, damaging those affected. Higher Rage Ranks make bigger splashes and Taunt the enemies in the area to attack you instead of your friends.
Hornet Nest

Hurl a nest of hornets at the ground, creating a swarm that attacks nearby foes. Higher Rage Ranks increase the area affected, as well as making the target sometimes panic and run away. (Fear)
Hot Foot

Set your target's feet on fire, causing it pain for several seconds after the attack occurs. At higher Rage Ranks, the target also suffers a Dodge penalty, making it easier to hit. Higher Rage Ranks also make this ability affect an area around the target.
Hunters Bow

This bow lets you fire arrows often and far, damaging your foe and slowing it down so they can't get to you easily. Higher Rage Ranks reduce the target's Footspeed still further and increase the duration of the effect.
Shark Attack

Groundsharks attack your foe, often knocking it away from you, and also causing some bleeding to persist after the attack. Higher Rage Ranks result in longer bleeding duration and sometimes paralyzing your target with shock. (Root)
Shuriken

Hurl spiny metal stars at your foes! In addition to damaging your target, higher Rage Ranks increase the effect to an area around your target, plus they cause your target to have reduced Accuracy for a time. Bonus Pun: Q: Can you hand me that pointy throwing star? A: Sure I can!
Solar Rays

Focus the power of the sun into a beam that damages your foe and, at higher Rage Ranks, can knock it away from you, or even stun it to Sleep for a short time.
Crowd Control
Duct Tape

Wrap your target up and keep it from moving (Sleep). NOTE: Hitting a target while it is taped will weaken the tape and allow it to move again. Higher Rage Ranks start affecting foes around your original target also, as well as increasing the chance that they get bound by tape.
Gumshoe

Make the feet of your enemy sticky and slow its Footspeed substantially. Higher Rage Ranks make this ring affect increasingly-sized areas and slow the targets within even further.
Quicksand

Cause the ground at an area to become mostly water and then solid mud for a short while, trapping your enemies where they stand. (Root). Higher Rage Ranks increase the area affected, as well as the chance to stick your foes in the mud.
Scaredy Cat

Make your foe flee from you in sheer panic! At higher Rage Ranks, this ring affects entire areas and the tendency for your foes to flee is bigger also.
Taunt

Sometimes, you need to pull enemies away from your friends. This ring does the trick, making foes in an area angered at you for a while. Higher Rage Ranks increase the area affected and the strength of the Taunt. The highest Rage Ranks also make your foes tremble, draining their Dodge for a time.
Defenses
Improbability Sphere

Use the Improbability Sphere to give you or a friend moderate defense (Persistent Armor), as well as to Reflect an attack back against the attacker of you or a friend! Any attack Reflected back on the attacker does the damage to the attacker instead. Higher Rage Ranks increase the amount of Armor and the probability that Reflection will occur.
Pot Lid

Use Pot Lid to give you or a friend moderate defense (Persistent Armor) and to sometimes Deflect an attack away from you or a friend completely. Any Deflected attack is nullified completely! Higher Rage Ranks make it more and more likely that a Deflection will occur on an attack.
Rock Armor

Cover each of your allies in Rock Armor giving them strong protection against incoming damage. (Armor Pool) The Rock Armor lasts for several minutes, or until it absorbs enough damage to break up. Higher Rage Ranks make stronger and stronger Armor.
Teflon Spray

This makes some of any incoming damage bounce away instead of hurting you or a friend (Persistent Armor). At higher Rage Ranks, it also makes your target harder to hit (Dodge) and eventually can occasionally Reflect an attack back against your foe.
Turtle

When trouble is overwhelming, the best thing to do is curl up in your shell and hope the bad things go away. This creates a protective field that can absorb an amazing amount of damage out of any incoming attack, but only lasts a short time. (Armor Pool) Higher Rage Ranks create stronger shells.
Healing
Bandage

Start a bandaging process on you or a friend. Healing then occurs over a short time, a bit at a time. Higher Rage Ranks increase the amount of Health recovered.
Defibrillate

Use this on a Dazed ally, and you'll instantly Awaken them. Higher Rage Ranks increase the amount of Health and Stamina recovered, as well as reducing the number of rings temporarily locked because you had been Dazed.
Diagnose

You analyze the wounds of all allies in the area around you and heal them of some of their wounds, including your own! Higher Rage Ranks increase the healing effect and the area affected.
Divinity

Use this to draw lifeforce energy to you more quickly, increasing the rate at which you and your nearby friends regain Stamina, even during combat! Higher Rage Ranks let you recover Stamina even more quickly, and the highest Rage Ranks even help you find loot more easily. (Luck)
Healing Halo

Create this halo over you and your nearby allies. You all then regenerate health more quickly, even during combat! Higher Rage Ranks increase this effect and the highest Rage Ranks also make all affected targets harder to knockback. (Weight)
Meat

Be a meateater and beef up big and strong! You heal a big chunk of damage you've suffered as well as increasing your maximum Health the same amount. Higher Rage Ranks increase the amount of Health increased.
Wish

Heal any of your friends, one at a time with this quickly-recharging and powerful ring. Higher Rage Ranks heal targets standing around your target also. The bigger the Rage Rank, the bigger the area affected.
Debuffs
Adrenaline

You jump up the nerves of your foe, causing them to jitter and shake, spoiling their ability to Dodge your blows for a time and causing them some damage. Higher Rage Ranks increase the Dodge penalty and deal more damage.
Knife Sharpen

You draw the keen edge from a foe's G'hi and use it to sharpen your own metaphorical knives. Your foe suffers an Accuracy drain for a short time as you disrupt its lifeforce and suffers some damage. Higher Rage Ranks increase the Accuracy penalty and deal more damage.
Buffs
Coyote Spirit

Use this ring to give you or any friend a faster Footspeed. Higher Rage Ranks increase the Footspeed bonus, as well as providing you the Luck of the Coyote (Luck).
Fitness

When you wear this ring, you just get better! Accuracy, Dodge, Willpower, Weight, Health Regeneration, Stamina Regeneration and even Luck are all given minor bonuses. This ring is passive and does not need to be clicked to be fully functional. Just wear it and it works!
Fleet Feet

Sometimes, you just need to get away. This makes you, and any friends around you, greatly increase your Footspeed for a brief time. Since you're probably running into or out of trouble, this also bolsters your Willpower with a modest bonus at higher Rage Ranks.
Ghost

You become slightly ethereal and matter occasionally, err, passes through you in a fairly disturbing fashion. (Dodge) Higher Rage Ranks increase the amount of Dodge bonus you receive. (Dodge bonuses also decrease the chance that a monster will Critical Hit you during a fight.)
Iron Will

When you fight a foe using Sleep, Root, Fear or other Willpower-based ability, Iron Will erects defenses around your mind (or the minds of any of your friends) to help you resist their evil influence. Higher Rage Ranks amplifies your mind still further, allowing you to Deflect occasional incoming attacks.
Keen Aye

Use this on you or a friend to help them spy out where a foe *will* be, letting you hit it more easily. (Accuracy) Higher Rage Ranks increase the Accuracy boost. (Accuracy bonuses also increase the chance that you will Critical Hit a monster on any particular attack.)
My Density

Are you getting knocked around by monsters? There's an easy way to solve that. Weigh more! Using this ring increases your Weight and sticks you to the ground. Higher Rage Ranks actually make you dense enough to resist some damage directly! (Persistent Armor)
Sweetheart

Blow your sweetheart a kiss with this wonderful ring and make them gush with giddiness. Sweetheart causes the heart to swell with emotion and increases maximum Health.
Fortune's Favor

This ring bestows its wearer with the luck of a golden rabbit, increasing the amount of loot they are rewarded with.
information on fortune’s favor and images of rings from http://zomg.wikia.com/wiki/Category:Rings
other ring descriptions taken from the help section within the zOMG game