A variety of colors complement brown, depending on its shade. Browns tend to be darker shades of oranges and reds, which are complemented by blues and greens.
According to the color wheel, browns can be darker versions of red, red orange, orange, and orange yellow. Examine a color wheel with secondary and tertiary colors, and notice that green is opposite red. This means that green and red are complementary colors. Similarly, blue green is the complement of red orange, blue is the complement of orange, and blue violet is the complement of orange yellow. To determine the complement of a specific brown hue, compare it to a color wheel, and see if it seems to contain more red, orange or yellow.
According to the color wheel on Adobe's Kuler tool, a redder brown is complemented by greener shades of blue, and browns with more orange in them are more complemented by lighter blues. For example, the chocolate brown B25B00 is a complement to the deep sky blue 00BFFF. Remember, complementary colors are technically opposites on the color wheel, but can also be used with analogous colors, which are closer to each other on the color wheel, so a chocolate brown, a sky blue and an orange can all look aesthetically pleasing together.