Award Snub: Many people did not take kindly to the band losing the "Best Rock Performance" Grammy to Imagine Dragons. Josh Homme even lampshaded this during a live performance soon after, jokingly announcing that he was performing an Imagine Dragons cover. Needless to say, the audience was not amused by this.
Broken Base: When the audio for "The Way You Used to Do" was released, the fanbase was pretty split on it, mostly because it was the first available song from Villains and it was very different from their other stuff. The fanbase mostly solidified again by the time the album released.
Era Vulgaris is pretty divisive, with opinions ranging from "a typically solid Queens of the Stone Age record" to "a major low point in an otherwise stellar discography." This is mostly due to the album's less mainstream and oddly mechanical/industrial sound. It doesn't help that the fan favorite Title Track was omitted from the final album and, instead, released as a B-side.
Ensemble Dark Horse: "You Think I Ain't Worth a Dollar, but I Feel Like a Millionaire" is one of the most popular songs on Songs for the Deafnote it probably helps that Nick Oliveri does a pretty good Metal Scream, but was never released as a single.
"Smooth Sailing" is the most popular song on ...Like Clockwork , and appears primed to be the next single.
Basically the entire first album. Until the reissue, it was extremely difficult to find, but is extremely popular in the fandom and contains classic tracks like "Mexicola", "Regular John", "Walkin' on the Sidewalks", "How to Handle a Rope", and "You Can't Quit Me Baby".
As for band members:
Nick Oliveri, known for playing naked on stage, being a druggie, a wife beater, and many other bad things.
Tear Jerker: "I Appear Missing," which seems to be about Josh Homme's near-death experience and ensuing four-month bedridden depression during the recording of ...Like Clockwork.
"How to Handle a Rope", despite being freakingawesome the lyrics are seriously depressing.
Their cover of "Christian Brothers," like Elliott Smith's original.
"I Never Came".
"In the Fade" is this in a much more existential manner. Despite our attempts to hold onto life, we cannot. In the end we all die, and we just have to accept it. We have to just, as the song says "Live till you die."