In a bathroom, there is usually a light or lights, an exhaust fan, and at least one receptacle. Although some bathrooms seem relatively small, that doesn't mean that everything can be put on one circuit. In fact, there must be a different circuit for the receptacle(s) than the one for the lights and fan. This means a minimum of two circuits.
Here's where it gets tricky, so check with your local electrical code officer to verify what you need in your part of the country. Some codes will require that the bathroom has its own circuits, not shared with other rooms for lighting and outlets. However, some can share circuits in other areas.
In some areas, it is required that outlets and lighting must be on GFCI protected circuits. I can see this being a great safety addition due to the fact that bathrooms are usually a wet environment and electricity and water do not mix!
Some local codes may require only a GFCI receptacle for safety, while others may require that all the circuits in the bathroom be protected by GFCI circuit breakers. Electrical safety is always an issue when dealing with wet locations especially.