Burgundy is sorta in the red family, though - our family room has a lot of burgundy rather than the cranberry color. I like red geraniums at the front door.
I use burgundy in my informal living room, along with dark blue and some greens. In the formal living room I went for blue checks, which was a drastic departure for me. I have nearly always gone for earth colors. I love yellow and green, and add in some orange and red in the fall.