So their new photo book is the closest fans will ever get to seeing the band again.
ABBA: The Official Photo Book (Weldon Owen Publishing) chronicles the foursome's history through more than 600 photographs.
"I'm not a nostalgic person, but looking at these pictures really took me back," founding member Bjorn Ulvaeus said.
The authorized photographic biography, which features numerous photos from the height of the band's career in the 1970s, was released earlier this year in Europe, and just recently in the United States.
In an interview, Ulvaeus said that although the band never officially broke up, they won't tour again - a sentiment he's echoed in the past.
"We took a break in '82, and it was meant to be a break. It's still a break and will remain so," Ulvaeus said. "You'll never see us onstage again."
And money doesn't talk, he said. The Swedish pop group - which includes Agnetha Faltskog, Benny Andersson and Anni-Frid Lyngstad - reportedly turned down nearly a billion dollars for a reunion tour, and they have vowed to never write an autobiography.
"We don't need the money, for one thing," Ulvaeus said. "Usually the reason bands have reunions is that one of them is destitute and the others want to help. Fortunately that has not happened to us."
Fans around the world can experience the band's music through the award-winning musical Mamma Mia." And Ulvaeus is proud of that, though he acknowledges being skeptical.
"For me it was like an experiment," he said. "Could you actually write a musical backward using the existing songs with the ground rule that you cannot change the lyrics?"
The show opened on London's West End in 1999 and became Broadway's ninth longest-running show after opening in 2001. In addition, Mama Mia has played more than 40 cities around the world, and was adapted for film in 2008.
Ulvaeus laughs off the idea of a sequel, but says anything could happen.
"You never know, it depends if there's a very good script," he said. "There have always been rumors, but nothing that I can confirm or deny right now."
