There are two types of agranulocytes:
Lymphocytes are much more common in the lymphatic system, and include the so-called "natural killer T-cells". The blood has three types of lymphocytes: B cells, T cells and natural killer cells (NK cells). B cells make antibodies that bind to pathogens to enable their destruction. CD4+ (helper) T cells co-ordinate the immune response (they are what becomes defective in an HIV infection). CD8+ (cytotoxic) T cells and natural killer cells are able to kill cells of the body that are infected by a virus. T cells are crucial to the immune response because they possess a unique 'memory' system which allows them to remember past invaders and prevent disease when a similar invader is encountered again.
Monocytes share the "vacuum cleaner" (phagocytosis) function of neutrophils, but are much longer lived as they have an additional role: they present pieces of pathogens to T cells so that the pathogens may be recognized again and killed, or so that an antibody response may be mounted. Monocytes are also known as macrophages after they migrate from the bloodstream and enter tissue.