Our family was always nearly a full generation behind with gaming and I suppose I still am, it's cheaper that way. :3 But when I was young, we just didn't have anything during the proper NES era. I'd go to a neighbor's or cousin's house and be transfixed, but I'd never be allowed to play myself. I worried I'd mess up, even if given the chance.
We did eventually get a NES some time before the SNES came out, but by that time I'd already seen most of the popular titles. I was drawn more to the niche oddballs like Golgo 13 or Faxanadu and creepy games like Castlevania or Ghosts and Goblins which my sisters also loved. When I had shoveled driveways, mowed lawns and walked dogs enough for my own 16-bit system, it was Phantasy Star and Sonic on the Genesis that caught my eye rather than Mario or Zelda, with which I'd never forged a personal connection. Those had always been someone else's games, Sega's library was offering to be my games.
I was nearly an adult by the time I got acquainted with my younger sisters' and best friend's SNES, so I did eventually catch up, but it was too late for me to feel the same nostalgic kinship with the bigger series. Luckily, they were young enough to have games available to them and not have to go through the same barriers to gaming itself that I did.
Like many other girls, poor kids and kids whose cultures didn't interest game marketing, there were a lot of times we were shut out, but we still managed to find our interests despite that. Gaming is a strong enough medium that you can make a connection if you have the interest. But for those that were unlucky, felt too shut out to develop that initial spark, I seriously hope we're on the path to greater accessibility if not far enough already.