You can tile over a subfloor of thick plywood but make sure is it solid and even and be very wary about getting the subfloor wet (especially in a bathroom) as it will swell and break the tiled surface.
If you are laying onto anything other than screed or concrete then make sure you use a suitable flexible adhesive as ordinary tile adhesive will not cope with the flexing of the surface due to heat, moisture and presure.
I have just had my bathroom done and we had ceramic floor tiles laid on 1/2 inch "MARINE-QUALITY" plywood (nailed down at 6 inch intervals) with flexible adhesive. As for wall tiles - my tiler said that provided that they are sound - the best surface for wall tiles is an existing tiled surface.