Preventing mold growth in your bathroom is pretty easy, especially if you are starting with a clean slate; that is, a bathroom that has no pre-existing mold or water damage problems. New constructions are having more and more problems with mold actually being built into them, though, so if you are having a home built for you, you should make sure and have a mold inspection done around the middle of the process to make sure it is not getting built into your new home. Even though mold may start to grow in these rooms due to using bad quality materials, if the building is technically up to code, there is nothing that you can do to make the contractor compensate you.
If you are starting with an older home, like most of us have, then you likely have a few problems with your current bathroom, especially if the previous owners did not take care of it. If you see cracked tile, missing grout, or caulking, you can bet that water has gotten to the subfloor and it could be water damaged. Try bouncing up and down on your toes a bit and see if the room shakes. If it does, you might want to check under the house and see if the joists are weak or damaged. If they are, bet on having to replace the floor and either putting back the materials you had above it or replacing them, too.
Mold is not only a problem on the floor in the bathroom; it can also be a problem on the ceiling if there is nowhere for the steam given off by the bath or shower to go. Most building codes require that a bathroom have either an exhaust vent or a window to let out steam to help maintain the cleanliness of the space, but older homes were not constructed this way because the code did not exist. Even if your bathroom does have a window, it still does not let anywhere near all of the steam out of the room, so having an exhaust vent installed is the only real way to do this.
Your shower curtain also will start to mold after a while if you bunch it into a corner of the bath tub like most people do. Either avoid doing this and spread the shower curtain out so that it dries completely or keep it cleaned with a product such as Tilex that kills mold and mildew.