When I was growing up I used to rummage around in the bookshelf in our sitting-room (there was a set of Jane Austens, a set of H.G. Wells, Grimms' fairy tales, and assorted books my father had bought through a book club) and just read the ones I liked the look of. This was as well as having my own children's books in my room and going to the library. I think my parents would read to me before i could read on my own, but they really just let me graze apart from that, so even just having the books there was a big advantage. But in some ways I would say the correlation is probably the other way round - intelligent parents have books in the house, and their children in turn have a better chance of turning out intelligent too! (but some might say they probably would anyway)
Likewise, our house is filled with books and musical instruments, and my older son is a very good pianist and works in the field of high-performance computing, and the younger one is a very good writer (and film-maker - not sure where that came from!). But again I don't know which way round the correlation goes.