Illusory Ring of the Conqueror
Makes left hand weapon invisible. Finish the game without dying.
Illusory Ring of the Exalted
Makes right hand weapon invisible. Finish the game without using a bonfire.
Open the King's Gates. This is needed to complete the game anyway, but you'll find it after the battle with Velstadt. Loot the corpse in the next room to find it.
Strengthens thrust weapon counter attacks. Obtained from defeating Old Dragonslayer.
Increases maximum HP. This is found near the Cardinal Tower bonfire in Forest of Fallen Giants. Head to the room near Pate--the one with the ballistas. Climb the ladder down here to find a door you can't open. But wait--attack the door, and soldiers on the other side will open it for you. Take them out, then open the chest in here for the ring.
Can also be chosen as a gift when starting the game.
Life Ring +1
Increases maximum HP. This is found in the Iron Keep. From the Threshold Bridge bonfire, move ahead into the keep proper. When you reemerge outside, follow the left balcony to a greatbow-wielding knight. You'll have to first drop down the corner here to access the ladder, but when you do, you can climb up to the knight's perch and find a chest containing this ring.
Life Ring +2
Increases maximum HP. This is found near the Crumbled Ruins bonfire in the Shrine of Amana. Proceed through the area until you're near the next fog gate. Instead of going through, follow the left edge of the area to some branches you can bust through. Back here is a cyclops; kill it, then loot the nearby corpse for this ring.
Lingering Dragoncrest Ring
Increases spell duration. Can be purchased from Straid of Olaphis at the Straid's Cell bonfire in The Lost Bastille.