One of the worst is that fucking Sound of Silence cover Disturbed did. Completely destroyed the intent and melancholia of the original and turned it into another whiny, angsty, nu-metal fagfest. Can't understand why it got the acclimation it did.
Best? Gotta mention the obligatory Hurt by Johnny Cash to get it out of the way. A few others I thought were really good were Metallica's cover of Turn the Page, Bob Dylan's cover of Mr. Tambourine Man, Iron Maiden's cover of Cross-Eyed Mary, and Pearl Jam's cover of Last Kiss.