Which of the cell types commonly found in mammals has the greatest number of mitochondria?
It's commonly believed that it's muscle cells that have the largest amount of mitochondria, and for good reason.  Muscle cells are continually used to move the body, so they have the most mitochondria because of the large energy requirement.  If you want to be more specific, the muscle cells of a marathon runner have even more since the muscle cells involved in running need to be able to do a lot of aerobic respiration.  Another example is the cells in the heart; the amount of mitochondria makes up 40% of the cell.

The truth is, retinal cells with photoreceptors most likely have the most (80% of the cell volume) since they need to reset the potassium/sodium pump to keep the action potential in the nerves the same.   

If you're curious, the cells with the least amount of mitochondria are skin cells and erythrocytes (red blood cells) since skin is just a protective barrier and red blood cells don't need to exert any effort or energy to move.

Sources:


http://hyperphysics.phy-astr.gsu.edu/hbase/biology/mitochondria.html
http://www.ncbi.nlm.nih.gov/pubmed/12511073