With little thought given to the matter, I've come up with my list, which is all earlier stuff since that's all that immediately comes to mind. Much of my knowledge of Dylan's music is based on what other artists have recorded since I discovered Dylan the artist after he'd been around for a while. I will name the songs and the versions that I was initially most familiar with in somewhat chronological order. Here it is with links to the songs available if you click on the song titles:
It Ain't Me Babe -- I'd heard mention of Bob Dylan in the teen magazines in the early 60's, but had not heard his music. Then, I heard Johnny Cash's version of "It Ain't Me Babe" and thought it was utterly cool. My curiosity about Dylan was stirred and my appreciation of Johnny Cash was secured.
Don't Think Twice It's Alright -- I first heard this song when it was released by The Wonder Who, which was a sort of joke pseudonym of The Four Seasons. This version was a sort of joke cover version of "Don't Think Twice". In fact the entire album was almost a joke since one side was cover versions of songs by Burt Bacharach and Hal David while the flip side was songs by Dylan. The Four Seasons singing Dylan? I was in my early adolescence and this was my first exposure to Dylan. It wasn't all that bad actually and I was a big Seasons fan back then.
The Times They Are A-Changin' -- Seems like everyone was singing Dylan songs back in the sixties. I first heard this song as a good time sing along on Beach Boys Party album. Later the Byrds did a version that I liked even more.
Tears of Rage -- This song was on The Band's Music from Big Pink album. It's co-written with Richard Manuel, but I'm including it here anyway since it's one of my favorite songs.
I Shall Be Released-- Also from Music from Big Pink, this Dylan song has been oft recorded.
All Along the Watchtower-- I was blown away by the Hendrix version of this Dylan song, but I've come to prefer the mellower sound of Dave Mason's version.
I Want You-- This was one of the first Dylan songs where I actually began to prefer Dylan himself performing his own songs.
Like a Rolling Stone-- It's a good song and I like it.