In the traffic pattern, what is the appropriate distance from the runway for the downwind leg?
Most instructors say that (in a low wing plane) you should see the runway on the tip of the wing or between the tip and 1/4 in the wing. AOPA has a nice over view of non towered airports here. This FAA brief states it should be flown 1/2 to 1 mile out (page 7-4 of FAA Airplane Flying Handbook, FAA-H-8083-3B). 


  This leg should be
  approximately 1/2 to 1 mile out from the landing runway,
  and at the specified traffic pattern altitude.