I find that songs from my pre-high school days still hold meaning for me, because they're no longer played on the radio, and I don't listen to the old CD's in my collection that much. So when I do hear them, they still have some meaning.
When Napster came around, I was one of the first to discover it (seriously). I used it primarily to find rare b-sides or live performances of my favorite bands. For me, it wasn't until I got an iPod and iTunes that I constantly listen to music. And like rabicle said, there are some songs that don't mean anything to me, because I can easily buy an album on iTunes and listen to it instantaneously.
I think what it comes down to is finding music that you really like and that you can relate to. As you can see by my avatar and signature, my favorite band is Garbage. If someone were to ask me why though, I'd have no idea. It's something about the music. One of my other favorites is U2. After seeing them live, they are undoubtedly the best modern rock band. And now, I hear their songs in a new way after seeing them live, and it has meaning for me. I saw them in New York City in October of 2001. When I got off the train at Penn station, everything seemed so different. There were posters of people who had died in the World Trade Center everywhere, and the whole mood of the city seemed different. I'm getting goose bumps just thinking about it now. So whenever I hear U2 now, it brings me back to New York, and how it's the greatest city in the world.
When it comes to relating to music, I find that there's always a couple songs I can relate to when I turn on the radio. And recently, there's been a resurgence of rock music with new bands like The Killers, Franz Ferdinand, and Modest Mouse, to name a few. Green Day put out the best album of 2004 (fluck Ray Charles and the Grammys. He only got it because he's dead). U2 just put out a new album, as did PJ Harvey and Wilco. And Garbage's new album is coming out in April, and it's a return to the rock sound of their debut. I'm LOVING the music scene right now, because it seems that the pop craze has died down, and there's been a return to real rock music. (And I'm not talking about that nu-metal crap either)
I had something I was gonna say at this point, but I went back to change something at the top, and now I forget. Oh well.