Do cataracts tend to run in families? Both my parents had them and my grandmother did also.

No. Cataracts are usually a sign of aging. It's like getting gray hair and wrinkles -everyone gets them, it's just a question of when. Somethings can make them come on sooner, like diabetes and steroid use, but really it's just a matter of time.
Genetics cataract. A history of cataract at a young age often runs in families. Most patients though get visually significant cataract around the age of 70. A history of no cataract in your parents and grandparents may not mean that you will avoid cataract because the standards used in the past were more strict (ripe cataract). This is because the surgical risk was higher and benefit lower at the time.