I usually don't wear any but when I do I use coconut oil. It works really great on taking off the most stubborn makeup and it also hydrates the skin around your eyes or wherever you used so it works as a dual product. It's also not expensive to buy and a jar of it lasts you a very long time.
I use a waterproof eye makeup remover of whichever brand, most usually work great for me and a separate cleanser to remove my face makeup. My current cleanser is Philosophy's Purity Made Simple but I used to swear by Clinique's cleanser from the three step system.