In residential construction how far away are rafters installed from each other

16" center to center is standard.

Rafters as in roofing rafters?I have spaced them anywhere from 16" to 48"

Commonly,I have them at 24"o/c

spacing of roof rafters depends on size,span and where you live.most commonly normal kilm dried 2x stock is 16 on center

What size of drywall would you use to keep from sagging

Presumably you mean what thickness drywall is used for ceilings. That most often would be 1/2" for ceiling joist on 16" centers.