My personal favourite eye makeup remover is Merle Norman's Luxiva Dual Action Eye Makeup Remover. It is extremely gentle on the eyes and removes evvvverything.
As a suuuper cheap and convenient alternative, a small dab of olive oil removes heavy-duty makeup like a charm! Just dab the area with a qtip, gently rub in with a finger, and wipe off with a tissue.
Also, when I'm all out, I find that a TINY dab of Johnson & Johnson's baby shampoo works extremely well too! Dab on a tiny dot of baby shampoo, very gently rub it in, and rinse with water and a face cloth.