The best paint color combinations are those that use analogous or complementary colors on a color wheel, or that mimic the colors of nature. Personal preference ultimately has a lot to do with what color combinations look great or are unacceptable.
Color theory is the science of color and it offers two useful tools for combining colors; one is the color wheel, which shows colors in the order they are found when white light is separated through a prism. A color wheel have just the three primary colors of yellow, blue and red, or it can show dozens of shades. The paint strips commonly found in hardware stores are portable versions of color wheels.
Color harmony uses the wheel to find the best color combinations; analogous colors are any three that sit side by side on a 12-part color wheel. Using a shade of each color -with one as the dominant shade- achieves an excellent color combination. An example could be green, light green and yellow to create a kitchen with a garden feel.
Complementary colors are those that sit across from each other on the color wheel. On a 12-color wheel, light green and light purple are examples. Using shades of these two colors could create a cheerful children's room.
Exceptions to the color wheel theory include white -which goes with almost anything- and black, which can be paired with several shades. Using combinations of earth tones, such as shades of browns, greens and blues, can be quite relaxing and make an excellent paint choice for bathrooms and bedrooms.