Bathrooms can be a problem if moisture constantly forms on the walls from hot showers, etc. If this is the case and the existing paint is peeling or mildew has formed, these issues should be resolved before any paint is applied. Kill mildew with a 10% bleach water solution using the process, Killing Mildew before Painting.
Peeling paint on bathroom walls is usually caused by moisture between the paint coat and the wall surface. To repair this damage scrape off all loose, peeling paint and wall material. Seal the surface with a shellac–based primer/sealer and repair the damaged wall material. See Repairing Water Damage, Skim Coating Techniques and the other wall repair articles at Drywall and Plaster for repair help before painting.
When the walls are ready, prime any repair compound with flat latex paint or latex primer and let it dry completely before applying alkyd–based, or shiny finish paint like semi–gloss. In bathrooms with a chronic moisture problem, where previous wall damage has occurred, use alkyd-based finish paint to help block future moisture penetration. In bathrooms with recurring mildew, mix a mildew retardant –available at paint stores– into the finish coating.
In bathrooms that don't have an existing moisture problem it's best to use latex paint on drywall and plaster walls and ceilings. Contrary to popular belief, latex paint does not peel when exposed to moisture. Latex actually breathes much better than alkyd or oil paints, particularly flat latex. This breathing allows water vapor to move thru the paint coat and wall material preventing trapped moisture from causing a peeling problem. See Paint Brushing Techniques and Paint Roller Techniques for application help and Paint Coatings Defined for more about paint coatings.