Neutrals are limited to gray, brown, black and white. Gray and brown are very commonly seen on roofs, so if you're going for a look that won't draw attention to your home, these are very safe colors to pick. In general, gray looks better on a home already painted in cool colors like blue and green, while brown looks better on a home already painted in warmer colors like red or orange. Meanwhile, black and white, while neutral, are attention grabbers because they're so bold.
Use earthy colors in a wooded environment to blend your home with the surroundings. Earthy colors include brown, gray-blue and some shades of green, like sage green and olive green. These types of colors often complement a home made from natural materials like wood and stone, but earthy colors are very common even in urban or suburban environments.
Contrasting color pairs are those colors found opposite each other on the color wheel. For example, if your home is made of red brick and you choose to paint the roof green, you're choosing a contrasting color. This is a bold choice and not appropriate for every situation. Study the color wheel for ideas.
Bright colors like blue, red and orange are very uncommon for obvious reasons: they're hard on the eyes and tend to detract attention from the other aspects of the house. However, there are advantages to painting your roof a bright color, including the ability to easily direct visitors to your house and the fact that you'll probably have the most memorable home on your street, if not in your whole town. This bold move can make or break the appearance of your house, so proceed with caution.