Archive Panic: There are only ten official studio albums (counting the two forthcoming volumes of Teargarden by Kaleidyscope), so that doesn't seem too bad. And then you look at the band's colossal vault of B-sides and reissues. There are 114 tracks in the Rarities and B-Sides compilation alone, and that's not a complete representation of the band's works. And then you look at the reissues. Adore and The Aeroplane Flies High are the most expansive of these thus far, containing six CD's and a DVD each, which are all filled to the brim with bonus goodies. The running time of the reissued Adore alone is over nine hours. In short, good luck.
Note that there are still probably dozens of hours' worth of material left in the vaults. The Aeroplane Flies High contains a twenty-three-minute-long track called "Pastichio Medley", which is a collection of snippets of tracks from the Mellon Collie era that didn't even make B-side status. There are about seventy of them. Of these, two are formative versions of songs that eventually got released either on Mellon Collie or The Aeroplane, and a dozen more were eventually released on the 2011-2014 reissues. The remaining ones are mostly not available at all, though a few others have been bootlegged. It's quite plausible that similar amounts of material were left over from the other albums' sessions, or possibly even more, considering that Mellon Collie was a double album (and that around an additional hundred minutes' worth of material, excluding the medley, made it to B-side status). Say what you will about Billy Corgan, but he's mind-bogglingly productive.
From Oceania: "Quasar" was the moment at which people realized the Pumpkins really were back.
Better Than Canon: When Billy Corgan put out the Adore box set re-release in 2014, it included a mono version that was the original idea for the album. Some fans wound up preferring that to the stereo release.
Corgan, on Machina: "Adore didn't alienate the audience, they were just sort of like, 'Oh, it's not the record I want.' [Machina] alienated people."
You can easily start a debate among fans as to whether or not the second time around, starting from Zeitgeist to Oceania and whatever comes after that, is considered truly The Smashing Pumpkins or just In-Name-Only.
Ensemble Darkhorse: "Drown" to the Singles soundtrack. The song received airplay despite a) Never being released as a single, and b) Being the only song on the album by a band from outside Seattle.
"Muzzle" is one of the band's post popular songs despite only being a promotional single, never even getting a full single release or music video.
Mellon Collie has a lot of these: "X.Y.U.," "Thru the Eyes of Ruby," "Bodies," "Where Boys Fear to Tread," "Jellybelly," and "In the Arms of Sleep" all arguably qualify.
"Set the Ray to Jerry" is quite popular despite never being on a full-length album (it was the closing track on the 1979 EP).
The band has a lot of B-sides that qualify as this. "Obscured", "Starla", "Cherry", "Let Me Give the World to You", "Here's to the Atom Bomb", etc. One of them ("Rotten Apples") even wound up being the title of the band's greatest hits compilation.
As far as albums go, Adore certainly fits these days (although the Pitchfork review of the reissue, which gave it an 8.5 and Best New Reissue, argues that it's cited as "underrated" so often that that can't possibly be true anymore). Machina II probably fits too, as it's generally regarded as a substantial improvement on the album to which it's a sequel.
Epic Riff: The live version of "Daphne Descends" has a truly glorious one.
Also, the intro and main riff from "Cherub Rock".
"Zero," "The Chimera" and "Siva" have some killer ones too.
"1979", "Rocket", "Soma", "Bullet with Butterfly Wings", "Silverfuck", "Set the Ray to Jerry"... they have a lot of them, really.
Face of the Band: Billy Corgan. May also be crossed with I Am the Band as he's the only original member left. Second place was James in the early days and Nicole more recently.
Fan Community Nickname: "Ghost Children", based on the story of Machina / The Machines of God; also, "Pumpkinheads".
Harsher in Hindsight: Back in 1995, as Mellon Collie slogged through a long development process, Corgan declared that "it either will be our last album, or it will be our last album as people know the Smashing Pumpkins." While it did not end up being their last album, it was the last album to feature the original lineup, as Corgan ended up firing drummer Jimmy Chamberlain for drug abuse during the ensuing tour.
James Iha appearing as a guest on stage for a few shows in 2016, after apparently not talking to Billy since their last show in 2001. Billy revealed later on that he'd been in friendly contact with D'arcy earlier in the year too.
Jerkass Woobie: Corgan may be a jerk at times (as attested by throwing Pavement off a festival bill because their song "Range Life" mocked his indecipherable lyrics, his transphobic insults against custom pedal manufacturer Devi Ever, or his bizarre declaration about wanting to "piss on Radiohead" and constant insults thrown at his former bandmates), but he has had a pretty tragic life, having grown up in a horribly abusive home, spending much of his childhood taking care of his disabled brother, and dealing with severe depression, even contemplating suicide. He may be a control freak and a jerk but he seems to be desperately holding onto the only good thing in his life.
Signature Song: either "1979," "Today," or "Bullet With Butterfly Wings".
Vindicated by History: Corgan predicted that this would happen to Adore, and over a decade after its release, he appears to have been right.
Corgan has also mentioned that he regrets having described the album as "electronic", believing that this distorted the way people perceived it, and once commented that he believed that simply referring to it as an "acoustic" album would have caused less trouble (the album only really had one electronica song while the singles retained "1979"'s use of technology.)
The band as a whole. They were The Scrappy of alternative music for a while during the '90s for their Arena Rock influences (and Corgan's general dickery didn't help), but are much more positively viewed nowadays.
Wangst: Billy Corgan is very prone to this in his blogs and interviews. It seeps into the lyrics sometimes, but is generally considered forgivable because of the music.