What gauge of wire do you need to run off a 20-amp breaker?

For a 20 amp breaker 12 AWG conductors are standard. However, depending on distance you may need to use a larger gauge conductors.

What gauge of wire do you need to run off a 20-amp breaker?
Depends what way the cable is mounted, the required length of the cable, and where you are (US, Europe. etc.)

For a 20 amp circuit you should use 12 gauge wire. For a 15 amp circuit, you can use 14 gauge wire. For long runs you should use the next larger size wire.

Have a look at this website for detailed inofrmation. (http://www.epanorama.net/documents/wiring/wire_resistance.html)