I think it does, but it certainly isn't necessary.

My mother is a physicist (although in a different area than me) and my dad is a mathematician. That meant that there was a lot of discussion about math and science at the dinner table. Plus, whether I wanted it or not, there was plenty of 'help' on science/math homework etc. I would say that it was also helpful in that my parents could put me in touch with other scientists that I could talk to about their work and what they were doing and get advice etc.

I will say, however, that having scientist parent(s) sometimes puts a bit of pressure on the kid to go into science, whether the parents mean to do it or not. But that's probably true for most professions.

I definitely think there is an advantage if one or both parents are scientists. But I also think that having parents who stress the importance of an education and who encourage their children to be curious is also important. My father was an electrician who worked on Lockheed's C-130 airplanes, he was also very good at math. My mother was mostly a house wife, sometimes an office worker, but she helped me to read at an early age and encouraged me to work hard to get what I want out of life.

OK, this is fun to talk about. But I do want to stress what Mitzi said -- fostering curiosity and education is just key. My dad (who was an attorney) was always saying, "how do you know that?". My mom was a very very early computer programmer (I grew up with punch cards around the house....does anyone reading this even know what those are??) and later ended up being a statistician and toxicology researcher. Most importantly, though, from a very young age I recall walks outside where we never really got anywhere, just turned over leaves, watched stuff swimming in small ponds, or sat out gazing at the stars. Nothing that cost much (although I did get a chemistry kit once - and yeah, kinda made some messes and stinks), just a lot of "why", "how come?" and "so how do we know that?" type of discussions. With my own kids when they were small, each had to come to dinner prepared with a question. We usually got sidetracked and off topic during the discussions and rarely got to address everyone's questions of the day, but the point was to (1) come up with questions, and (2) participate in the discussions of "why", "how come?" and "so how do we know that?" And yeah, my kids are pretty drawn to science....although not solar physics at all.

I've seen it go both ways, where you have the child of scientists go on to be a great scientist themselves, but I've also seen the children of scientists go in completely different directions and show no interest in science at all. The same as I've seen children of non-scientists become great scientists. Whatever your family history is, I don't think it needs to restrict or define you. They key in my opinion, is to find role models for yourself. Scientific parents can be great role models, but if you don't have that, then go and seek out others who are. My high school teacher was a role model for me, and when I got to college, the early-career researchers were always inspirational. Find a grad student or undergraduate to help give you some advice. Your inspiration and motivation comes from YOU but it can be enhanced by anyone else.

I have heard about many scientists who have parents that are scientists, engineers, or medical doctors. However, there are also lots of scientists and engineers whose parents did not work in these fields. Neither one of my parents had careers in science.