Can I use a Presta tube in a Schrader rim? I keep losing pressure in my tires, and among other things, I'm looking at the valves in the tubes. It's an old mountain bike with 26 inch tires. Can I use Presta tubes on rims drilled for Schrader valves? I know the valve will be smaller than the hole and could cause issues there, but has anyone had success (or failures) with this?
As you mentioned, one of the primary differences between a Presta and Schrader valves are the diameters--with Schrader valves being slightly larger--and therefore the valve holes on bicycle rims are drilled to suit one size or another.

Your foremost concern with using a Presta valve in a rim drilled for a Shrader valve shouldn't be 'movement' of the valve stem, as geoffc suggested, but rather a 'hernia' of the tube through the excess space at high pressure, leading to a blowout.

Most mountain bike tires sit at a low pressure, therefore you will probably get away with it, however, there is a very inexpensive adapter, sometimes called a 'valve grommet', which is made out of rubber or metal and serves to make the valve hole small enough for a Presta valve to fit snugly. It will also not come loose under high pressure, unlike geoffc's 'old tire' solution.