Some colors, which go well with dark brown, are mellow yellow, rusty orange or light grey. Other nice colors that would match up with dark brown are cream, white, glossy black and red. Red is a bright and cheery color that would work well to contrast the darkness in the dark brown color.
Brown is a neutral color so really any color can go with it. It has to do more with the statement you want to make. Jewel tones can give a sophisticated look. Earth tones a more subdued look. or creams and whites for contrast statement.