Codes
From a legal perspective, building codes are set locally in most cases, so it can be difficult to say what the general requirements are. The 2006 International Residential Code, for example, requires some type of ventilation in the bathroom, and many local codes have similar requirements to ensure a safe and healthy environment in the bathroom. From the common sense perspective, using a vent is a good idea, no matter the local codes.
Rust
Most bathroom fixtures have plating and coatings that keep them from rusting. But sometimes coatings can wear off, and older bathrooms may have metal fixtures that do not have as much rust protection. Without a vent in the bathroom, moisture floats around in a contained space. This makes it much easier for rust to form and can quickly damage unprotected fixtures, bolts, metal linings and other components.
Mold
For more modern bathrooms, rust is not the primary concern. That excess moisture, without any vent to draw it out, can seep into tile cracks, drywall and other porous surfaces, making it very easy for mold to grow in these spaces. The mold will permanently damage these materials and may spread to other areas of the house, not to mention posing dangers to health.
Placement
While you do need to install an AC vent in your bathroom, there a range of options for placement. A floor, ceiling or wall vent will take care of the moisture problem and help cycle air through your bathroom. A window that you can open to create air flow may also be acceptable if you do not have the room or money for a venting system.