My grandmother had one of these, as well. She lived in a small town in far west Texas, surrounded by pump jacks and oil fields. The shelter (or cellar, as it was later called) was always stocked with jams and canned goods, and as kids we would occasionally go down there to play, if we could manage to brave the spiders.
The thing I realized as I got older, though, was the psychological impact that the threat of nuclear war had on that generation. My grandmother was not wealthy -- she worked most of her life at the cafeteria of the local high school -- and her husband died when he was in his 30's, leaving her to raise 5 children. At some point they decided to spend not-insignificant amounts of money on building a bomb shelter. As I grew up, I realized that this had a subtle but profound impact upon the attitudes of my grandmother and her children: they were all just a little paranoid, careful to the point of it almost seeming neurotic at times. My cousins and I did not share the same fear about the world at large that we witnessed in our parents, and came to believe that this was due to the fact that we grew up in a world where nuclear threats were not so pervasive.
It all tied back to the bomb shelter. The mere existence of this cinder block-lined hole in the ground was a daily reminder of what could happen, and what they believed would very likely happen. Many of my aunts and uncles were also prone to believe in the apocalyptic scenario de jure, from upcoming depressions[1] to stockpiling food and water in preparation for Y2K, to more extreme beliefs about race wars and the second coming of Christ.
Anyway, this shelter had an impact on me at a young age, but in the opposite direction. It taught me that living in fear like that is no way to live.
[1] http://en.wikipedia.org/wiki/The_Great_Depression_of_1990