On one hand, I think that ignoring older music is pretty stupid; I don't think anyone is so naïve to think that only the X-number years of their lifetime produced good music.
That being said, in thinking about my response, I realized that the majority of music that I listen to that predates my birth are artists that directly or indirectly influenced modern bands that I like: Bowie, Eno, Suicide, King Crimson, Tubeway Army, Modern Lovers, Love, Throbbing Gristle, Kraftwerk, Can, Neu!, etc., etc. The only exceptions I can really think of are 60-era girl groups and bluegrass (which I don't have any albums of, but it’s pretty much the only music I listen to on the radio: thanks, NPR!).
I don't know if that's 'cause I'm disinterested in things that didn't influence the "living" music I've directly experienced in my lifetime, or because it's simply easier to evaluate older the music in the context of what I know (i.e., it's easier for me to determine that I'll probably like Kraftwerk because they've influenced so many bands I already like than Sinatra, who as far as I can tell, hasn't had much influence on bands in my collection).