Well that question has a very cheap, easy to find answer: Baby Oil! Or mineral oil if you want to be more grown up about it.
No seriously, that's all I have been using for months now. Every night (except those exceptionally lazy ones) I take one of those flat round cotton pads, cover the centre with baby oil, and wipe everything away! This works so well I almost never need to use more than one cotton pad. You do then need to wash the oil off of your face afterwards, but that's the case for most makeup removers. When I am feeling extra lazy, I use a second cotton pad with witch hazel on it to wipe the oil off and call it a day (A post on the wonders of witch hazel will be in the near future as well).
The baby oil I have been using is called Teddy's Nounours Unscented Hypoallergenic Baby Oil, but any brand would work just as well. I do recommend that you make sure it is at least unscented though, just in case. I don't remember the exact price since I bought it months ago now, but it was definitely less than $5 for a 592mL bottle. That is insanely inexpensive! On top of that I have maybe used 1/6 of it so far, and that includes the day I knocked it over and spilled a lot on my floor. At this rate I will probably not run out for another year or two!
I definitely suggest you give this stuff a try. Even oilier skinned people might want to give this a shot. Since you are washing all the oil off immediately after, it doesn't really have time to sink into your skin at all. And if you don't like it as a makeup remover, try shaving your legs with it! I do that occasionally when I want extra soft legs, and it works wonders. At that price, what have you got to lose?
Edit: A few days after I wrote this another beauty blogger did a post about the very same product. In it she explains the reasons why most people don't want to use mineral oil and why these reasons are myths. Her name is Robyn and I really like her blog. It has an awesome mix of makeup and chemistry, so I suggest you check it out!
Here is a link to her post about mineral oil: Beauty Myths: Should You Be Worried About Mineral Oil