My parents and I listen to narrowly similar things: Radiohead, Joy Division, The Smiths, The Cure, Echo & The Bunnymen, R.E.M. (mainly their Columbia stuff), Siouxsie & The Banshees, Manic Street Preachers (although they seem to prefer post-Richey stuff whereas I like both) etc. And of course the titans, Beatles/Zeppelin/Pink Floyd/Bowie/Who/Hendrix/Stones/Kinks etc., and some punk (Clash, Jam, Buzzcocks). Nothing much after Britpop though. Radiohead and Placebo were probably the last bands they got into (maybe Coldplay as well). Other than that they seemed to lose 90% of any interest in contemporary music when I was born (early 90s) and have since mainly just bought CDs of bands that were the shit in the 80s (in the UK Indie Charts) that continued to make albums in the 90s and 00s.
We're into pretty much the same things, and I'm not sure whether this is embarrassing or not (maybe less so for Generation Y?). My impression of what's cool to like to is heavily influenced by them on an unconscious level and I'm not sure if this is a good thing. It's not a good thing because it means I have little attachment for anything that doesn't fit under their invisible seal of approval, but what they liked when they were in their teens and 20s is just so... cool!
However I found it a bit of a shock when my dad said he doesn't like My Bloody Valentine.