Take your home's architectural style and surroundings into consideration. A seaside Cape Cod style home is traditionally painted in grays and blues; use warm browns and reds sparingly if at all. On the other hand, a country lodge surrounded by trees will harmonize with the environment painted woodsy browns and reds.
When choosing colors to complement existing siding, such as red brick or brown stained wood, think beyond basic red or medium brown. Complementary colors---those opposite each other on the color wheel--tend to work well together. While red and brown are not complementary, you can still liven up each color by choosing a cool brown with gray or blue undertones to go with warm red brick or sizzling glossy red trim to set off deep brown siding.
Visit a paint store and look through paint swatches. You'll notice the wide range of browns and reds and that some are cooler and others warmer. Combining them livens up both colors. Another way to add contrast is to combine a light brown with a dark red or a pale red with dark brown. Adding white trim or a third color for impact will make your home stand out and is a good way to define the roof line with white gutters or attractive wood windows with creamy white paint.
Since you can't accurately predict what colors will look like on the exterior of your home from the little swatches, testing the paint on your home is important. Once you have narrowed your color choices to a few shades, pick up 1 qt. of each paint. Paint large test samples on your house. Give yourself a day or two so you can assess them in different lights (and to give your neighbors a chance to chime in).
If you get stuck trying to find the right color combination, go to a paint store and ask what color literature they have available. Most paint companies print up brochures with suggested exterior color schemes--they may not be on display, so you need to ask.