I saw these on My Happy Crazy Life and thought that this would definitively be something I could do.
If you don't want to make them, Amazon sells a brand called Better for Grownups Organic Cotton Rounds.
*** UPDATE ***
I don't know why I haven't tried these earlier! They are the perfect size for washing your face, removing nail polish, etc. I was able to make 12 in 45 minutes using flannel material I already had. Each square was cut into a 4 in x 4in piece. Wrong sides sewn together with 1/4 in. seam; turned and top stitched. Since they were so easy to make, I have them in glass tumblers in both bathrooms.