Avon's eye makeup remover is an excellent and affordable solution to removing stubborn cosmetics. I am thoroughly impressed with it's ability to remove waterproof mascara and eyeliner (cosmetics that I wear often).
All you need if a little bit dabbed onto a cottonball and it's able to remove everything that a normal facewash might not be able to. A second swipe over the eyes with a clean cottonball will remove anything that the product soaked one might have left behind.
Pros - effective, affordable (about $4 - watch for sales, I think I picked mine up for like 99 cents), only need a small amount of product, clean/fresh smelling, lightweight feel on the skin (feels like lotion), it isn't oily like some makeup removers, bottle lasts forever!
Cons - Leaves a very light residue (which I just remove with a splash of water at the end of my routine), other than that, the only thing I can think of is that it is inconvenient to have to pay shipping on items like this (makes them more expensive than they should be), so get on Avon's email list - they are always sending out free shippng codes, deals, etc.