Yes, there are living organisms that do not have cells. These organisms are primarily classified as viruses. Unlike cellular organisms, viruses are not made up of cells; they consist of genetic material—either DNA or RNA—encased in a protein coat. Because they lack cellular structure and cannot carry out metabolic processes on their own, they are often considered to be at the edge of what we define as ‘living.’
Viruses require a host cell to replicate and propagate, which differentiates them from living organisms that can reproduce independently. Examples of viruses include the influenza virus, HIV, and the coronavirus.