Award Snub: Never won a Grammy Award, despite a few nominations in the alternative category. It took them until 2019 to be inducted into the Rock & Roll Hall of Fame, despite being eligible for 15 years beforehand.
Big-Lipped Alligator Moment: Their 1982 - 1985 period where they released 'Let's go to bed', 'The Walk', and 'Lovecats'. The former two are synth-pop songs that capitalized on the electronic dance craze at the time, and the latter being a strange jazz song.
Dork Age: Fans commonly see Wild Mood Swings as the band's weakest release.
Many fans agree that Wild Mood Swings could have actually been a good album if some of the weaker tracks were replaced with underrated B-sides such as "A Pink Dream". The self titled album and 4:13 Dream also have fan backlash to them. Some fans believe that the self-titled, with the exception of its well-liked singles "The End of the World" and "Taking Off", is even worse than Wild Mood Swings.
Ear Worm: "A Forest", "Lovesong", "Lullaby", and "The Hanging Gardens" among many others.
In the UK, "Close To Me" is one of the group's most enduring radio staples - but in its 1990 "Closer Mix" (or more commonly, the "Closest Mix", which is the shorter edit version) rather than the 1985 original. In the US, the best known version of the song is also a remix: The single version of the original, which added a horn section that is not found on the album.
Conversely, very much averted by the 1986 "New Voice - New Mix" version of "Boys Don't Cry", which became Canon Discontinuity almost immediately following its release. The original version wasn't a hit, the "new mix" was - but you'll only ever hear the original played these days.
Germans Love David Hasselhoff: The signature keyboard-bass-drum patterns of "Close to Me" became the popular "Cure riddim" in Jamaica, rehashed as the backing track for numerous Reggae songs.
Harsher in Hindsight: "Killing an Arab." They don't perform it anymore, unsurprisingly (or when they do, they change the lyrics around heavily; some of the alterations include "Killing Another," and more humorously, "Kissing an Arab.")
A less well known example: In the video for "Mint Car", the lead singer of The Associates, Billy Mackenzie, makes a light-hearted cameo, which gets a lot sadder when you find out what happened to him less than a year after the release of the single, which arguably makes the song itself more of a Tear Jerker, as even though it's one of the band's happiest and most upbeat songs, this gives it a slightly melancholy and bittersweet feel. It even led to Robert writing "Cut Here" which is arguably one of the band's most tearjerking songs.
Heartwarming Moments: "Lovesong." Robert Smith wrote it for his wife Theresa Poole and they've been married ever since. "I will always love you" indeed.
Misaimed Fandom: Enough of it for "Killing an Arab," that they had to put a sticker on Staring at the Sea to decry racist use of the song. In fact, it got so bad that their US label wanted to leave the song off the album altogether - the sticker was a compromise after Smith refused.
Replacement Scrappy: Arguably Jason Cooper. Even recently some fans of the band were still calling him a terrible drummer, just because he replaced fan favorite Boris Williams, despite the fact that by that time, Cooper was longer in the band than any other drummer (Williams, Andy Anderson, and Lol Tolhurst).