The best fence stain colors for your house may depend upon several factors. What color are other fences in your neighborhood? Are there regulations put forth by a homeowners association that limits the colors of fences? What color is your house?
As a rule, fencing for your backyard should match whatever you do for your front yard, if fenced. If only the backyard is fenced you can do whatever you want with color. You can do the traditional wood tones with stains or perhaps you'd like a white fence to match the white picket fence around your front yard.
Wrought iron fencing is traditionally black. This is because most wrought iron fences are created in black and the color penetrates through the steel. Older neighborhoods may have wrought iron fences in colors to match the trim of a historic home to add curb appeal and a bit of punch to your home.
Wood fencing for the front yard can be rustic to go with a log home and retain wood tones. The traditional white picket fence is the most common wood fence, but again, in historic areas, homeowners are painting their fences to match the shutters or gingerbread trim on their house.