Does cancer run in the family?  It depends.  With some forms, a higher likelihood of acquiring the cancer runs in the family, if not the disease itself.  Let's examine this more closely.
 
As an example, breast cancer is a form of the disease which which relatives have a higher chance of getting it if someone else in the family got it. In some instances, this increased risk could be because of a genetic mutation.  Two examples of mutation are BRCA1 and BRCA2.  These cause a higher risk of breast cancer.  A woman with this mutation has around a 60 percent lifetime risk of getting breast cancer.  A woman with one of these mutations also has a higher risk of getting ovarian cancer.  The mutation is transmitted genetically to offspring in what is called an "autosomal dominant model." Put simply, this means the child of a carrier of a BRCA mutation has a 50 percent chance of acquiring the same mutation. 
 
 Unlike people who carry well-known mutations such as BRCA 1 or BRCA2, these people don't appear to have evidence of genetic differences / alterations which increase the likelihood of breast cancer.  The raised chance of breast cancer among these women could be linked with a group of genes, not just a single genetic mutation.  The genetic alterations together as a group might have an increased tendency to develop breast cancer.  We also can't easily dismiss environmental factors among these people. 

The role of these factors is hard to quantify, and how much of the raised risk is because of common factors in the environment is hard to determine.  If one woman has a mother, daughter or sister who was diagnosed with breast cancer, this woman's chance of developing it is 1.7 times grater when compared to others in the general population.  But if the relative with breast cancer had developed the disease before menopause, the woman's risk rises to 3-fold.  This illustrates just how difficult it is to determine what is a hereditary risk and what is environmental.
 
We can see something similar in colon cancer.  Some specific genetic mutations raise a person's risk of developing colon cancer dramatically.  One noted example is a mutating APC gene.  If someone carries this particular mutation, this person will have nearly a 100 percent chance of getting colon cancer in his or her late adulthood. 

This APC gene is transferred via an autosomal dominant model.  This simply means that offspring of the carrier will have a 50 percent chance of inheriting the same mutation, and thus a greatly increased chance of developing colon cancer.  Unfortunately, most instances of colon cancer are not with genes which can be tested.  But we can say without qualification that a colon-cancer diagnosis in any individual increases the chances of colon cancer developing among is close family.  Just as with breast cancer, this isn't because of any single genetic factor, but because of interacting among a group of genes and several environmental factors such as eating habits.
 
So what we conclude is that some predisposition toward developing some cancers are transferred genetically.  However, in many cases the reason one family produces several people with cancer could also have to do with similar habits and environments.