This ability prevents 1 damage from each source an opponent controls each time that source would deal damage to you. It prevents 1 of any damage, not just combat damage.
Spells and permanents have controllers, but cards that aren't on the stack or the battlefield don't. If a source without a controller (such as a cycled Jund Sojourners, for example) would deal damage to you, 1 of that damage is prevented if an opponent owns that source.
The effects from multiple Guardian Seraphs are cumulative.
Standard: Ej legal
EDH / Commander: Restricted
Extended: Ej legal
Pauper: Ej legal