I would argue in most cases that music sounds better on vinyl than on CD, but it's a taste that I devloped quite recently; growing up, I was all about cassettes and then CDs, and never once complained. It wasn't until some time in college that I started paying attention to vinyl, and anyways what really inspired me was the desire to hang John Denver's Greatest Hits on my wall. (I don't think I know of another album that emanates just absolute pure joy.)
I've really come to believe, more fervently than about Denver or Springsteen or whatever, that classical music sounds exponentially better on vinyl than on CD. I have always hated listening to classical music – and I've been playing it on piano for years and years and years. My parents had a decent collection of piano and orchestra works, and I detested all of it. Lately I have been buying some of my favorite pieces on vinyl though- for example, Chopin waltzes, which I own on CD also. And by "own" I mean "stole from my parent's shelves." I discovered that the elusive "warm" tones, which sort of defy description even though everyone knows what it refers to, make a world of difference to the sound of a concert hall. The music comes alive in a way that I've only previously experienced while playing it myself. And as for the symphonic works, it has all of a sudden become listenable.
I thought for a moment that maybe I've just grown up a little, and am beginning to acquire the taste for the genre. Maybe it is just all those years of classical music study and academic obssession paying off. But when I try to listen to some stuff on CD that I have, it simply isn't the same. Maybe it appeals to the experience of the performer, because the slightly muffled fuzziness seems more tangible than digital perfection. Maybe lending it that antiquated sheen is sort of like a sepia-toned photograph, enhancing the appeal through an implicit sense of nostalgia.
ADDITION – 3/29/06 – Bob Dylan writes in Chronicles: Volume One: "Folksingers, jazz artists and classical musicians made LPs, long playing records with heaps of songs in the grooves- they forged identities and tipped the scales, gave more of the big picture. LPs were like the force of gravity."