What other types of immune cells are there and how do they contribute to immune-mediated killing mechanisms?

Professional antigen-presenting cells such as dendritic cells, macrophages, and B cells1 are instrumental for the activation of adaptive immunity. These cells internalize antigens either by phagocytosis or receptor-mediated endocytosis, processes them, and then presents them on their surfaces as part of major histocompatibility complexes (MHCs). This mechanism is essential for T cell maturation and activation.
Natural killer (NK) cells (not to be confused with natural killer T cells) are innate immune system mediators of cytotoxic cell death. NK cells are somewhat similar to T cells, with the notable exception that NK cells do not require MHC presentation or antibody binding to recognize and eliminate target cells. This makes NK cells critical for tumor cell surveillance.2
Neutrophils are the most abundant type of leukocyte in humans, and comprise an important part of the initial innate immune response. Neutrophils possess both phagocytic and cytotoxic (via granulation) capabilities, and play significant roles in the induction of acute inflammation and wound healing mechanisms.1 For additional information and related topics please visit our dedicated immunotherapy section in our resource center. 

1. C.A. Janeway Jr., et al., Immunobiology: The Immune System in Health and Disease. 6th edition. New York: Garland Science; 2005.
2. I. Waldhauer and A. Steinle. “NK cells and cancer immunosurveillance,” Oncogene 27, 5932-5943, 2008.