Tan color matches very well with blue, purple, burgundy, cranberry, turquoise, brown, orange and green.
Tan is basically light brown -- a tertiary color made by combining red and green or orange and blue.
Tan is a neutral color which could go with everything; it can provide a softer look on its own or serve as a background for another color.
Complementary colors are colors directly opposite each other in the color spectrum or wheel. These colors are highly contrasting and look very bold if put together. Such combinations usually draw the eye and stand out very well. Blue is opposite of orange on the color wheel. That is why gold, rust and brown compliment shades of blue.
Learn more about color harmonies. Check out the basic techniques for combining colors at Tigercolor.com.