Try lavender or violet. My neighbor has brown eyes and when she wears lavender eye shadow, her eyes just pop! I never really liked brown eyes before until I saw the way they look with light purple eye shadow.
You can use just about any color.. even blue in lighter or darker shades.. brown hues look great as well as deep burgundy or grey.. Green is fine too, as long as it is not too bright of a green!
This all depends too - what look you are going for!