Icy Gull and Buzzer have called it with The Byrds and Cash. The Band obviously worth a mention also and Manfred Mann made a career out of it. I was always partial to this, although was never bothered by any of their own songs:
Rod Stewart has always been a Dylan fan and did quite a few covers on his early albums. Here's a Dylan song covered by Rod that Dylan never actually included on any of his own official albums and is only found on bootlegs and anthologies
The genius of Dylan is in the lyrics, his songs should rightfully be covered again and again. It's like reading poetry. Many are stories that grow and develop in the re-telling. It's great to here different voices interpret his words and sound brilliant doing it.