You’d die, obviously. But how quickly and what of? What would be the first things you noticed if your cells stopped regenerating?
Would you just appear to age really quickly, seem fine then drop dead or what?
Probably similar to the symptoms of chemotherapy or radiation poisoning. Stomach lining cells are some of the most rapidly-dividing cells and among the first you’d notice were gone with nausea and vomiting an all that. Anemia as your blood cells are no longer being replaced. Hair loss as your hair follicles are no longer working.
On the plus side, any cancerous tumors you might have had will be the first to die. 
I think you’d win first prize in any Zombie contest. 
This will happen to the first person who ever reaches the age of 140 or so. Complete cellular replicative senescence (the Hayflick limit) will occur, and all cell division will stop. Cells do not immediately die when they reach this point, but they have a tendency to malfunction chaotically. There currently are people actively researching ways to get these cells to work properly again. Some gerontologists aver that the first person who will ever reach the age of 150 years has already been born.
Wow!