Complexions (light, medium and deep) with stunning golden or olive undertones, should use a brown shadow that has more warmth to it, such as a gold, rose gold or even rust. My favorite brown shadow to play with in this color realm is the Giorgio Armani Eye Tint in Senso. The color is rich, buildable, and so gorgeous to complement those golden and/or olive undertones! It can also be used as an eye primer! Pro Tip: Run a little bit of warm brown or gold under your lash line, along the bottom lashes — this will keep your eyes looking balanced and defined.
Neutral or beige undertones also come in all skin depths, from cooler tones to warm ones. This lovely skin tone is one that can get away with almost any brown shade. My favorite brown eye shadow palette for neutral skin tones is the Urban Decay Naked2 Basics. The browns in this palette are magical! They blend easily and can take you from day to night in no time.
For the beauties with pink or red undertones there are a couple of ways to play with browns on the eyes. One way is to accentuate the warmth of the undertone, and use browns with a mahogany richness (which will also make eyes of any color pop). I'm obsessed with the L'Oréal Paris Infallible 24 HR Eye Shadow in Bottomless Java for this look.
Complexions with pink and red undertones can also work with shadows with more of a gray or charcoal tone, creating a nice contrast with the warmth of your natural skin tone, and delivering a more ethereal look. Try the L'Oréal Paris Infallible 24 HR Eye Shadow in Continuous Cocoa! Pro Tip: Use the pad of your finger to apply the shadow to your eyelids for a more pigmented finish. Make sure to blend with a large fluffy eye shadow brush at the end to maintain a nice fade out.
Although certain tones of brown do work better in theory for different undertones, my biggest rule of thumb with cosmetics is, if it makes you feel gorgeous, then keep rocking it out!