I hope this doesn't confuse you, but in one sense, yes, heavier bodies do fall faster than light ones, even in a vacuum. Previous answers are correct in pointing out that if you double the mass of the falling object, the attraction between it and the earth doubles, but since it is twice as massive its acceleration is unchanged. This, however, is true in the frame of reference of the center of mass of the combined bodies. It is also true that the earth is attracted to the falling body, and with twice the mass (of the falling body), the earth's acceleration is twice as large. Therefore, in the earth's frame of reference, a heavy body will fall faster than a light one. 

Granted, for any practical experiment I don't see how you'd measure a difference that small, but in principle it is there.

Why do objects fall at the same acceleration?
I work as a kitchen aide in an assisted living community. I assist the cooks in some aspects of kitchen prep (mostly non-cooking), but occasionally I help in the actual cooking of food. For breakfast, oatmeal is served every morning. The residents enjoy the creaminess of the oatmeal when milk is added, but for those who are lactose intolerant I cannot take that risk. So what alternatives to milk can I use to create a creamier oatmeal? 
