Most colors pair well with brown eyes, but purple and blue tones provide a contrast that makes darker eyes pop. Green eyeshadows are especially complementary for brown eyes on the hazel side. In general, matching the eyeshadow to the color of the flecks in the eye's iris will help bring out a person's natural eye color.
Even within the same color palettes, a color can have different tones depending on if it is a warm or cool shade. For example, green can have gold flecks in it, giving it a warm tone, or silver, which cools the shade down. Any color with a silver cast will contrast well with the warm tones in brown eyes.