I'm rewiring a bathroom, and will install a GFCI receptacle on a 20 amp circuit breaker (dedicated to the bathroom only). I am also going to have a fan and vanity light on the same circuit, downstream of the GFCI outlet (the fan is above the tub, thus requiring GFCI protection). Question: downstream of the GFCI outlet, am I required to continue to use 12 AWG cable for the rest of the circuit, or can I switch to 14 AWG? A code citation would be most helpful along with any rationale for why this allowed/not allowed, whether this is a good idea/ terrible idea, etc.
Yes, all conductors protected by a 20 ampere circuit breaker must be at least 12 AWG copper. There are a few exceptions and loop holes, but none of them apply to your situation.
National Electrical Code 2014
Chapter 2 Wiring and Protection
Article 240 Overcurrent Protection
240.4 Protection of Conductors. Conductors, other than flexible cords, flexible cables, and fixture wires, shall be protected against overcurrent in accordance with their ampacities specified in 310.15, unless otherwise permitted or required in 240.4(A) through (G).
(D) Small Conductors. Unless specifically permitted in 240.4(E) or (G), the overcurrent protection shall not exceed that required by (D)(1) through (D)(7) after any correction factors for ambient temperature and number of conductors have been applied.
(5) 12 AWG Copper. 20 amperes
The rationale here, is that 12 AWG copper conductors are rated for 20 amperes, whereas 14 AWG copper conductors are only rated for 15 amperes. So if you put 20 amperes through a 14 AWG conductor, the conductor could heat to dangerous levels.
That would make it a terrible idea to use 14 AWG copper conductors, on a circuit protected by a 20 ampere circuit breaker.