If you don't have history of the "C" word in your family, are you less likely to develop it?

Probably. One of the standard questions asked by doctors, including oncologists, is, "Do you have a history of cancer in your family?" They wouldn't ask if it wasn't relevant.

The good news is that cancer treatment has developed such a long way that cures are much more likely these days, and they're making progress all the time.

There are some cancers that have genetic links. For example with breast cancer there is the BRCA gene. Having that gene can increase you chances of getting breast cancer but still isn't a guarantee you will get it or just as not having the gene won't guarantee you won't get breast cancer. I do not have the gene, but even with my family's history, and my lifestyle , I still run a high risk for breast cancer.