The coefficient depends on the two materials and especially on the impurities on their surfaces. For example take copper and copper. "Clean and dry" 1.21. Thick oxide film .76. Sulfide film .74. These values serve to illustrate how variable the coefficient can be. If you cleaned the copper perfectly and stuck the two surfaces together in a vacuum, you would get a huge coefficient because essentially the two pieces fuse together into one continuous copper piece.
Vargo, it would be worth expanding upon coefficients greater than unity since this implies a greater force required to slide the object than to simply lift it off the other surface and move it along, supporting it in thin air.
Good point Studiot. But consider rubber on rubber. Doesn't it seem plausible that picking up the rubber and moving it through the air would be less work? Check out http://www.engineershandbook.com/Tables/frictioncoefficients.htm for other particular examples.
I don't know a lot about this personally, but I can try to faithfully paraphrase R. Feynman in "Lectures on Physics". If you have two surfaces of the same pure substance such as copper and you are somehow able to eliminate all impurities separating them, then they can bond together and form a continuous metal piece. Apparently this can be observed at home with glass on glass. If you put a bit of water between the surfaces it can lift the impurities out of the way and allow the two pieces of glass to bond together in places. If you then slide one along the other, you will notice nicks in the glass where the two pieces of glass were ripped apart.
I don't know how this phenomenon would affect the coefficient of friction between two different materials like copper and steel, but it at least serves to illustrate the tricky nature of the coefficient and its dependence on "hidden variables" such as surface impurities that could vary depending on the exact situation.