I guess it is the ultimate sign of recognition for an artist when a fellow artist makes a song about you. Dylan got two of such dedications. One from Syd Barret, one from David Bowie! This is a quite interesting topic, and here are the songs that I know which are dedicated to an artist. Let me know if you know others too!
Song to Woody - From Bob Dylan to Woody Guthrie
R.A.M.O.N.E.S - From Mötorhead to Ramones
Song For Bob Dylan - From David Bowie to Dylan
Bob Dylan Blues - From Syd Barret to Bob Dylan
Buddy Holly - From Weezer to Buddy Holly
Song to Bobby - From Cat Power to Bob Dylan (Thanks to Thuan for this one)