Mitosis in human body
In many cases cell division depends on the stage of development an organism is in. The rate of cell division is obviously much faster in a developing organism and from what I understand fully differentiated cells such as neuron and those in skeletal muscles don't divide (correct me if I'm wrong here).  

In early development totipotent cells (stem cells that can become anything) begin to differentiate dependent on environmental factors, turning into multipotent (partially differentiated) cells that can only lead to certain cell types. For example: mesodermal precursors can differentiate to myoblasts, which can go on to differentiate into myotubes, later forming muscles. 

Epithelial and and blood cells are the two of the main types of cells that need to be constantly replaced in developed organisms. As far as I know cells lining the gut epithelium are fastest to divide. They are created from stem cells in 'crypts' (pockets) in the lining and are pushed outwards, where they are later broken down (by what I would assume would be abrasion and intestinal juices). My book gives them a lifespan of 3-5 days. External skin cells are much slower to divide (though I'n not sure by exactly how much). 

Red blood cells have have a lifespan of approximately 120 days. They are replenished by stem cells in the marrow of certain bones (e.g. a femur). Neutrophils are the next most common blood cell, with a circulating life of 8 hours (but lifespan may be a few days). Per day, roughly equal numbers of RBCs and neutrophils are created and are most numerous new cells created per day. Lymphocytes, another white blood cell, are responsible for immune 'memory' can persist for years. The fastest recorded mitotic cycle for a mammalian cell (in culture) is ~8-10hrs.