Two things constrain the amount of current you can carry in a wire:
1. Voltage drop
2. Heat generation
With smaller circuits and lower currents voltage drop is the main thing to be concerned about. Simply take the wire you are considering, find out its size (gauge) and length, determine the resistance and then use Ohm's law to find the voltage drop for the current it will carry. See if this voltage drop is within allowable limits. If not, use a thicker wire.