Almay Eye Makeup Remover Pads, $7.00, are pretty much perfect. The cute little screw-top container makes it easy to travel with them, and most importantly, they do exactly what they are meant to do. Sweep one pad over a closed eye and your waterproof mascara, winged purple liner, or whatever else you wore will be gone. They are also very moisturizing, which is incredibly important. Keeping the eye area moisturized, as well as protected from the sun, helps fight off wrinkles.
There's no need to rinse afterwards, but dabbing the area with a tissue will get rid of the oily effect.