My favorite covers are often, perhaps not surprisingly, Dylan songs. To name just three:
1) Jimi Hendrix "All Along the Watchtower"
2) Byrds, "Mr. Tambourine Man"
3) Jason and the Scorchers "Absolutely Sweet Marie"
The first two will be familiar to most everyone. If you haven't heard the Scorchers' cover, I implore you to seek it out. It's on an EP called "Fervor," a record that surely belongs in the "canon."
Honorable mention: "Beat the Retreat"-An entire album of covers of Richard Thompson songs. It is superb.