Blue eyes: To make those bright blues pop you'll want to use warmer shades mixed with some deeper colors. I suggest dark purples, golds, and warm browns. I have blue eyes and I tend to stay away from black because it is often too harsh, I like to line just my top lid with a brown pencil.
*If you want to make your eyes appear larger just take white eyeliner and line your bottom lid*
Brown Eyes: To make your brown eyes pop make sure you use blues, violets, coppers, and greens. These colors may seem a little to out there for some people but don't be afraid of color! You may want to start off by using slight touches of violet to your eye shadow or use dark blue to line your upper lids.
Green Eyes: Green eyes are a little tricky but here's what I think, use black eyeliner to tight-line your eyes and stick to neutrals. Don't use light colors however because those will just mute the green color.I've also heard that purples really bring out green (and every other color it seems).