As kat says, you can see a big difference in the picture clarity of a good HD transfer over a decent DVD transfer. It can sometimes look slight when you're moving forward from watching upscaled SD to some of the worse-to-average HD transfers - until you've watched HD for a while and then switch back to SD.
You also get the advantage of access to an uncompressed audio track.
Maybe nothing that's particularly going to bother a casual watcher of TV and/or movies, but if you're into your AV you'll see the improvement as starkly as the jump to DVD from videotape. The uncompressed audio might be appealing to someone so heavily involved in music as you are?
I've had HD tv for more than a year now and, for me, the difference is worth the extra for the amount of shit i watch on the regular available channels
- especially on fast-moving things like sports and music gigs. You've mentioned that sports ain't your thing, so the improvement on that front's not going to impress you much, but as a music fan, it's worth going into a store to get a demonstration using music Blu-rays.
The only thing that bugs me at the moment is the relative lack of good music Blu-Ray releases, as that's my main thing to rewatch than buying films and tv shows, but it's obviously going to improve.