Rings described from left to right / top to bottom:
Slowly reginerates your health, at the expense of your magic meter.
Green Orb Ring:
Slowly reginerates your magic.
Blue Orb Ring:
Reduces the use of your air meter by 1/2, enabling you to swim beneath water or lava twice as long.
Silver Diamond Ring:
Increases your luck in finding bombs / arrows / health hearts / and magic jars
Decreases the damage you receive from enemies by 1/2 (not effective on spikes, drowning, or roasting in lava (when you dont have the fire charm)
Morning Star Ring:
Decreases your magic usage by 1/2
Reveals hidden paths and ghost blocks [at the expense of your magic meter.]
Gold Diamond Ring:
Increases your luck in finding coinage (money)
Again, let me remind you all, you can only have one ring equipped at a time. So there's no mixing of the varying powers.