again, minimimum tire size depends on the rim size.

one thing, I had a heavy old school mountain bike, a Specialized Stumpjumper from 1983, steel frame, non-suspension forks, the first year they sold them), and one year was using it for commuting, so went from the normal 26x2.125 knobbies to a 26x1.5" slick. it made that bike SQUIRRELY to ride, the light tire on the heavy bike was just unbalanced. a 26x1.9 was much more suitable.

there's a rim width table here, http://sheldonbrown.com/tire-sizing.html

I find you can go a notch or two WIDER, but you really shouldn't go SKINNIER. most cheap hybrids that come with 700x32-35-48-40 tires have 25mm outer width rims, these tend to be about 19mm inside width. Sheldon's table suggests 28mm is the narrowest tire you should use on that rim size. Also, as the tires get skinnier, the air pressure has to go up up and away, and cheap pinned hybrid rims will NOT do well with 120psi in them