Note: I don't have brown eyes, so I haven't tested any of these looks out, but they are from pictures that have worked or things I have read online. Lets get started!
So, brown eyes have it kind of easy, because you can wear pretty much any color you want. It might not be as easy to make it pop, but its possible!
Green
Just as brown eyeshadows will bring out green eyes beautifully, green eyeshadow or eyeliner will bring out brown eyes! To get the most out of this trick, use a deep, jewel-toned green or an emerald. A gorgeous suggestion is the Buxom Stay-There Eyeshadow in Saint Bernard for eyeshadow, and Urban Decay's 24/7 eyeliner in Covet for eyeliner.