According to Reference.com, cellular organisms that do not have a distinct nucleus, such as bacteria, are called prokaryotes. They are distinct from the eukaryotes, which are the cellular organisms that contain a nucleus.
In the three domain system, which is used for classifying biological life, organisms in the Bacteria and Archaea domains are all prokaryotes, whereas organisms in the Eukarya domain are eukaryotes.
Red blood cells, while not considered to be prokaryotes, also do not have a nucleus. This helps them to maximize space inside the cell for haemoglobin, which is essential in the transport of oxygen. By comparison, white blood cells do contain a nucleus.