Anucleated cells are the one which have no nucleus and are thus unable to generate daughter cells. The most famous one is the mammalian red blood cell/erythrocyte. This also doesn’t have other organelles like mitochondria and serves mostly as a distribution vessel which carry oxygen from the lungs to the body parts.
The only one celled organism that I know of that has no nucleus is Eubacteria.
The only anuclear cells I can think of in the human body are platelets and mature red blood cells. Immature red blood cells have a nucleus, but as they mature and are released into the blood stream they lose their nucleus. Nucleated red blood cells are not normally in the peripheral blood stream and are indictitve of disease.