I for one have always liked Metallica's version of "Turn the Page" (fun fact: first time I ever actually saw that video was during an MTV special on banned videos. It was on at like 3 o'clock in the morning and had viewer discretion warnings at the beginning of every segment. What was blurred out in this YouTube video was....not blurred out for that broadcast) better than Bob Seger's. Which is weird, because I'm really not all that big a Metallica fan, but I like their arrangement of the song a whole lot better.
Another artist I've never been too fond of is Michael Jackson. Especially 11 year old Michael Jackson. I heard a rather generic pop-rock version of "I Want You Back" a few weeks ago on the radio that I liked quite a bit better than the original, but I can't seem to find it again. I have no idea who performed it.
Then there's the obvious answer. Even Trent Reznor likes that version better.