Almost all cells divide and reproduce, whether through sexual or asexual reproduction. There are very few exception to this. Some examples of cells that do not reproduce include nerve cells, red blood cells or erythrocytes, and gametes (sperm and ova). The RBC do not possess a nucleus and hence are incapable of reproduction. The gametes are also incapable of reproduction after they exit the meiosis cycle. The nerve cells are very specialized cells and lack the ability to reproduce. This simply means that a nerve cell will carry on its specific role in our nervous system till it dies and this is the only activity to which it will commit energy (apart from usual maintenance). This is actually advantageous to us, since the nervous system works because of nerve cells' placement in a network. It they were to reproduce, a lot more cells will compete for the placement in this network, causing loss of energy and loss of specialization.
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