The smallest unit of life is a cell when life is defined as the ability to replicate oneself. An argument can be made for prions and viruses to be the smallest units of life and although they are able replicate themselves, they are unable to do so without a host. I would argue that cells in an animal or plant would be unable to replicate themselves without the oxygen and nutrients that they receive by being part of an overall system.
Another interesting thing to ponder is that mitochondria; the cell’s power source are capable of reproducing themselves within the cell body, but again, need the cell’s nourishment to be able to divide.
So this begs the question: what is the smallest unit of life that can exist purely on its own? Protozoa are single celled animals that, apart from the habitat they live in, are totally independent. My vote goes to the small, yet highly capable protozoa.