This question yields a grab bag of answers, most of which depend upon your definition of organ. An organ exists within a hierarchy of systems in our body that starts with individual cells that make up a tissue. An organ is two or more types of tissue. An organ system is a collection of organs that share in performing a function in the body, such as the digestive system. An organism is several organ systems together to form a whole being; like me, for example.
Out of all the suggestions for the smallest organ in the body, I am going to go with the lymph node. The lymph node is part of our lymphatic system, which has three important functions in the body: it removes excess fluid, it absorbs fat and fatty acids and transports them to our circulatory system, and finally, it creates white blood cells, the body’s soldiers against disease. Lymph nodes are all over your body and range in size from 2 millimeters to 1-2 centimeters long. They are tiny filters that look for disease causing microbes in our body. They contain reticular tissue; a structural web, that holds lymphocytes that will detect and destroy bacteria and viruses. When lymph nodes are working hard to fight an infection, they can sometimes become inflammed which is why you can feel lumps in your neck when you have a sore throat. They lymphocytes are constantly traveling in our blood stream, and as our blood stream and our lymph system are connected, the lymphocytes are constantly flowing into and out of our lymph nodes. When a foreign body (antigen) is detected, the lymph node is stimulated to produce plasma cells. Plasma cells are little bags of antibodies that reach an antigen and attach to its surface. Many antibodies can attach to a single antigen and these antibodies also cause the antigens to stick to each other, creating this massive ball of antigens and antibodies (I think of the game Katamari) which the body has different ways of recognizing and breaking down. One of the roles of macrophages; a type of white blood cell consume these large antibody/antigen complexes. The diagram shown here is a typical lymph node.
Another small organ that is considered the smallest by some is the pineal gland in the brain. It is about 8 millimeters long and its job is to secrete melatonin; the hormone responsible for regulating our sleep/wake cycles.