The smallest species of frogs is Paedophryne amauensis, which was actually just recently discovered (December 2011). It's 7.7 millimeters (0.303149606) inches and currently the smallest vertebrate known to man. Being just recently discovered, I wouldn't hold my breath about finding it in the hobby any time soon.
Regarding the smallest species available in the hobby, I would guess some sort of thumbnail dart frog. Spring peepers (Pseudacris crucifer) are tiny as well, about 2.5 centimeters.

Hope that helps somewhat.