Typically, cells that replicate and divide do so with spindle fibers that are generated from the centriole. However, many neurons (nerve and brain cells) do not have centrioles and so do not divide. One interesting thing to keep in mind though is that recently studies have suggested that generation of new neurons can occur in certain parts of the brain (called "adult neurogenesis"). The process for generating these new neurons is a little different from cell division however, since they arise from stem cells, which are pluripotent.