DIY
Vinegar works well on soap scum and mineral deposits, but rinse thoroughly, as it can corrode some fixtures and etch glaze on tiles. You can also try tea tree oil -- 2 drops tea tree oil with 1 cup water -- in a spray bottle. A natural antiseptic and fungicide, tea tree oil costs more than vinegar but will kill most types of mold and help prevent growth; as with all concentrated oils, it should be used with caution, as it can trigger allergic reactions if it comes into contact with skin. Pregnant women should consult a doctor before using it. You can also use the all-purpose cleaners recommended here.

Tips
To prevent mildew on tiles and grout, wipe down the shower enclosure every time you use it (wash the towel every few days). Leave the shower door or curtain partly open to encourage air flow. Clean the bathtub once a week with warm water; a mildly abrasive, nonchlorine cleaner; and a cloth or sponge. (Never use steel wool, stiff brushes, or strongly abrasive pads, which can damage the tub surface.) Bathtub rings are usually the result of oily bath products or a poorly functioning drain, so be sure to keep the drain clog-free and to scrub with a little abrasive cleaner after you use a bath oil. People with allergies or sensitivities may like commercially available steam or steam-vapor cleaners (which can be used to clean many surfaces around the house). The steam loosens grime, which you then sponge off, and it also kills bacteria and viruses.