Everything he recorded from 1961 to 1969 is more or less essential, starting with 'The Freewheelin' Bob Dylan' and running through to 'Nashville Skyline'.
Pick up 'Blood on the Tracks' and 'Desire' from the 70s. 'Oh Mercy' is the only really great album he recorded in the 80s. He started the 90s pretty well with 'World Gone Wrong' and 'Good As I Been To You', but excelled himself in 1997 with 'Time Out of Mind.' His post-2000 work has been pretty consistent, beginning with the brilliant 'Love & Theft' which is probably another essential. 'Modern Times' and 'Together Through Life' are both solid pieces of work, while 'Christmas In The Heart' is worth having, even if only as a curiosity.
Also, if you're looking for a Dylan live album, pick up the recording of his 1966 gig at the Free Trade Hall in Manchester, although, I think it's listed as being at the Royal Albert Hall. This is the famous 'Judas' concert. The first CD is all acoustic, while the second CD is electric, featuring The Band. Also, don't forget 'The Basement Tapes'.
Gradually decreasing the quality of my own obituary.