While wearing a ring of regeneration, a character's HP is healed by one every move that the turn counter is increased unless they would normally heal on that turn (even if wearing more than one ring). This allows a player to identify this ring by putting on the (noncursed) ring, throwing an object upwards <, and examining their healing rate. The normal healing rate without regeneration is some HP every few turns.
Especially at very low levels, this ring is valuable because it makes much faster game play possible.
Unfortunately, wearing a ring of regeneration burns nutrition very quickly: every odd-numbered turn your nutrition is decremented. Thus, a player should only wear one if he's hurt, or about to become so, or if he is satiated and wishes to become less satiated quickly in order to eat corpses for intrinsics.
Dropping a ring of regeneration into a sink produces the message, "The sink looks as good as new."