I used to be what one might term a Dylanologist--I own all of his albums and have read obsessively about the guy. Speaking of which, everyone should read his book-great stuff.
To get into him, I recommend:
-Blood on the Tracks. This album starts out with "Tangled Up In Blue" which is one of the greatest songs ever written. It's catchy and melodic and folky, so it's a great introduction to folk-Dylan.
I would follow that up with The Freewheelin' Bob Dylan which has Blowin' in the Wind, A Hard Rain's A-Gonna Fall, and The Girl From the North Country, which are all beautiful songs.
Then go on to "Bringin' It All Back Home," which is my personal favorite Dylan album. It has Mr. Tambourine Man, which is one of Dylan's most famous and in my opinion, greatest songs. Of course, it also has Subterranean Homesick Blues (from which the infamous Weatherman got their name --"you don't need a weatherman to know which way the wind blows." Also, Maggie's Farm and It's All Over Now Baby Blue are on this album.....
of course "Highway 61 Revisited" is the Dylan goes electric and betrays folk music album, that has Like a Rolling Stone on it. Other than that song, I really don't love this album. "Blonde On Blonde" was Dylan's follow up to Highway 61 and it's a million times better in my never humble opinion.
"John Wesley Harding" has my all-time favorite Dylan song on it, "Drifter's Escape" and it also has All Along the Watchtower, which everyone here knows b/c of Rattle & Hum. I like "Nashville Skyline," because it's kinda warm and mellow, although the only famous song off of it is "Lay Lady Lay."
Dylan's last 2 albums, Time out of Mind and Love and Theft are fantastic in a way that he couldn't have been when he was 25, so I'd recommend those as well....Dylan is just brilliant and I could type and type forever about his stunning lyrics and which songs on every album are great.
I would stay away from Desire, Saved, Shot Of Love, and Infidels--I think that's probably his weakest period.
whew. much love for Dylan.