I don't think it really matters. On their earlier albums, they were called Smashing Pumpkins, and then it was The Smashing Pumpkins, and now, with the release of their album Zeitgeist, it seems they have gone back to just Smashing Pumpkins.
I have all of their albums. The only ones I can't find are Machina I (but I do have a single from it) and their B-side compilation album, Pisces Iscariot. If and when I manage to find those albums, I'll update the answer.
Anyway, on their first albums, Siamese Dream and Gish, it's just Smashing Pumpkins. But starting with the release of their third album, Mellon Collie and the Infinite Sadness, it's The Smashing Pumpkins.
These are the CDs I have where they are called Smashing Pumpkins:
Gish (1991)
Lull EP (1991)
Siamese Dream (1993)
Disarm single (1993)
And these are the CDs I have where they are called The Smashing Pumpkins:
Mellon Collie and the Infinite Sadness (1995)
Lost Highway Soundtrack, "Eye" (1996)
The Aeroplane Flies High Boxed Set discs (1997)
A Very Special Christmas 3, "Christmastime Has Come" (1997)
Batman & Robin soundtrack "The End Is the Beginning Is the End" (1998)
Adore (1998)
Ava Adore single (1998)
Stand Inside Your Love single (2000)
But the album Zeitgeist (2007), the first album they've made since they broke up and reformed with different members, lists them as Smashing Pumpkins.
i,m smashing pumpkins every where i go
The smashing pumpkins got their name from people leaving their pumpkins out from Halloween and kids throwing the soft rotted pumpkins at there houses,hence the name smashing pumkins
the Smashing Pumpkins were inspires by artists like My Bloody Valentine, The Cure, goth rock, prog rock, and heavy metal bands.
The smashing Pumpkins in 1996.
Some people like Nirvana better and some people like Smashing Pumpkins better. I like Nirvana better. NIRVANA! N!
The Smashing Pumpkins was created in 1988.
The Smashing Pumpkins ended in 2000.
"Bullet With Butterfly Wings" by Smashing Pumpkins
i,m smashing pumpkins every where i go
Live Smashing Pumpkins was created in 2008.
The smashing pumpkins got their name from people leaving their pumpkins out from Halloween and kids throwing the soft rotted pumpkins at there houses,hence the name smashing pumkins
Perfect - The Smashing Pumpkins song - was created in 1997.
Today - The Smashing Pumpkins song - was created on 1993-09-30.
Zeitgeist http://www.amazon.com/Zeitgeist-Smashing-Pumpkins/dp/B000OQF6N6
what is an odyssey what about smashing pumpkins Blah Blah Blah Blah I like pie
Owata - The Smashing Pumpkins song - was created on 2011-05-04.
The String Quartet Tribute to The Smashing Pumpkins was created in 2007.