Although Faith No More seem to do fairly straight covers, which is something I normally consider a waste of time, I consider their choices interesting enough to get a pass, or maybe it's just that they can do no wrong! I mean, how many rock bands cover Metallica, or Black Sabbath, (and yes, I know FNM covered War Pigs early on), Faith No more are off digging thru the Bee Gees archive or introducing Sparks to a new audience. (yes this is all horribly biased because I think FNM are the greatest thing ever!)
My main rule for a cover version however, is that if you can't bring something new to a song, why bother doing it, the current tidal wave of sewage that is X Factor, American Idol etc, where they give people 15 minutes of fame for being a glorified karaoke singer is just very poor imo, and no, just doing everything in 'big band' style without a sense of irony doesn't count either.
As an example, here's the Polyphonic spree, covering Nirvana's Lithium, in a quite different style.