Lancome Bi-Facil eye makeup remover! I received a tiny free sample bottle in the mail a while back. One day while looking for something to wash the gummy clay feeling off my hands, I tested a number of different liquids and that was the best. It's a bit pricy but a little goes a long way and I figure, it can't hurt my hands if its actually designed to be used around eyes! I got mine at a makeup store at an outlet mall so it was a bit more affordable.
Goo-Gone also works great, but after I used it my skin felt sort of dried out, and after the Bi-Facil, my hands feel smooth and a little bit moisturized. Olive oil also works, and I suppose vegetable oil would too, but surprisingly Baby Oil gel did not work at all in my test.