I have been told unofficially that researchers suspect that there is an as yet unidentified mutation that affects the immune system and allows many different cancers to grow.
My family is part of a study of inherited kidney cancer. We have had three cases in my mother's family, and one more distant in my father's family. I, my mother, and her mother all had premenopausal endometrial cancer. My sister had kidney, lung and thyroid cancers; my mother had enometrial and kidney, her mother had endometrial and duodenal, her father had stomach cancer, and her brother had prostate and kidney cancers.. My father died of pancreatic cancer; his half brother died of multiple myeloma. One of my cousins has non-Hodgkin's lymphoma. All genetic tests have been negative, but the cancers in my family are almost certainly inherited--the cause has just not been found yet.
Signs that cancer in a family may be inherited are: diagnosis at a relatively early age (sometimes at an earlier age in succeeding generations), cancer in more than one generation, the same or related cancers in family members, more than one primary cancer in individuals, and tumors in both of paired organs (e.g. both kidneys).