I would say that I do, but I think it would be more accurate to say that I feel a sense of disconnect from my current generation in the US. I relate more to people who grew up in the 1980's, and people of my own generation from certain other countries.
I like the music, the movies, and some of the fashions from back then, even though I wasn't around.
As for today's culture... there are definitely new things being created that I identify with and enjoy. But they're no longer mainstream.
For instance, about 80% of the music I can listen to is from the 80's, mostly rock and pop music. Now, there's music that I can listen to from today, but it's mostly Gothic Metal, Power Metal, and Synthpop bands. Read: Nightwish, Within Temptation, Magica, Lyriel, The Cruxshadows, and Assemblage 23.
For some reason or other, these bands seem to have the same "quality" that I appreciate in mainstream 80's music, but don't seem to find in mainstream music these days.