Slow Train Coming was the first Dylan album I ever heard, I was a big fan immediately. Most Dylan fans consider that album as trash, although it certainly wasn't his worst, in retrospect I suppose I see what they mean, although I still disagree with that opinion.
The reasons I loved that album are many, but I think the reason I'm still a Dylan fan basically has to do with the man himself. It is undeniable that he has a crappy singing voice, like really crappy. Yet he pulls it off. That's part of the mystique that surrounds him, most people would have listened to themselves sing, hear how crappy it was, then just kind of pretend it didn't happen. Dylan, OTOH, just sang more and didn't even attempt to improve on it. It seems to me that he simply has to Sing, he's compelled to and that's what he was born to do, so he did/does it.
Then there are the lyrics. Pure poetry, sometimes profound, sometimes telling a story, sometimes only seemingly profound, other times who knows WTF he was trying to say, but always well crafted, interesting and from the heart.
His musical style also stands out. When you hear a Dylan song, you pretty much know it's a Dylan song from the Music alone. That's primarily speaking of his Rock stuff, it was only a few years back that I finally listened to his Folk songs and I just became I bigger fan. Suddenly the whole Folk vs Rock controversy made a lot of sense. Still love his Rock stuff, but his Folk music is just a few notches better IMO.