I know it's not Friday, but the question struck me today and I wanted to post it.
See, the saying goes that a good story works regardless of genre and setting. It doesn't matter if you have future space armies with giant space ships and mecha, or the fantasy warriors fighting the good fight against the forces of darkness. If a story is truly classic and good, it will have a way to work with both.
However, certain setting conventions make handling various aspects of a story easier or harder. For example, there is a special kind of energy to a gun fight that you just can't capture in a fantasy game. At the same time, the nuances of long distance travel can add a dimension of tension to games set in the far past (or hard sci-fi in the far future.)
So, for the stories you like to tell in game, how important is the game's time period?
For me it is not super important. For games I like character driven stories, and those are usually - at their core - a bit more basic then what a setting needs to hatchet things in either direction. That said, the time period often does color that most crucial question of "Who are you?" that ever character story asks.
How about you?