Older home, ceiling is white - walls beige-trim off white-what color whould i paint the crown molding?
I'd say dark brown if you have a lot of similarly colored accents in your room, I.e antique wooden furniture, darker wood on floors, or if you have none of these, you could always add some accents in dark brown around your room. I think that this would work for any color you choose, I guess dark brown is a favorite of mine. Stand back and look at your room, ignoring the walls and ceiling, and determine what color is most prominent.
Most of the time the crown is painted with the trim paint. It makes a divider between the walls and ceiling, and is the same paint/sheen as trim.
That said, there are no hard rules, but that is typical.