Text (PY+errata): {Tap}: Choose a color. Add one mana of that color to your mana pool unless any player pays {1}. Activate this ability only any time you could cast an instant. [Oracle 2009/07/08]
Each player (starting with the current player and going in turn order) gets the option to pay when this ability resolves. [Prophecy FAQ 2000/05/25]
If a player pays {1}, Rhystic Cave does not produce any mana, but is still considered to have been tapped for mana. Things which trigger of the land being tapped for mana (such as Mana Flare) will trigger, but things which try to replace mana production (such as Ritual of Subdual) will have nothing to replace. [DeLaney 2000/09/08]