This is the first in a series of posts, each of which will discuss one useful pair of complimentary colors. If you're not familiar with art terms, "complimentary" in this case doesn't refer to saying nice things about each other, but colors on opposite sides of the color wheel. Complimentary pairs of colors are useful because they typically mix to create neutral and near neutral colors. Since most of nature is composed of neutrals, any painter who is interested in subtlety instead of LOOK AT MY BRIGHT BRIGHT COLORS! needs to learn about working with neutrals. (Not that there isn't a place for high-chroma colors, but I think they are best used with restraint.)
My favorite complimentary mixing pair is raw sienna and ultramarine blue. With them, you can mix a lovely range of cool blues, warm browns, and neutral greys. These colors don't call undue attention to themselves, but they harmonize well with each other and with a wide range of other pigments. It's a valuable exercise to do a whole painting with just these two colors and white; you'll be amazed at how much you can do with them. I've done lots of paintings in which those two colors predominate, staying in the background and setting the stage to allow other, brighter colors to stand out beautifully. Since both of them vary a bit from manufacturer to manufacturer, it's worth comparing a few of each with each other. At the moment, in oil, I use Williamsburg Italian raw sienna and Studio Products ultramarine. They mix very well together.
Update: Williamsburg also sells their Italian raw sienna as a pigment; it's the nicest raw sienna I've seen.