well, since theoretically people could wear more than one ring upon a finger ... I would Hypothisize for Ring limit (for one person) to be either 10, 15, 20, or 30.
honestly I think 16 would be the best number, because that is one for each finger, and then an additional ring for each of the primary three fingers (excluding pinky and thumb).
Edit: Some games might explain that Rings of Power are too hard to control if you have too many, restricting either each finger to only one ring, or more usually, restricting ring usage to 2 or 4. The idea being that the energies of the hand can only contain the power of 1 or 2 rings before losing all sanity (or being unable to bridle the powers of the rings, damaging the hand in some way perhaps).