I've heard ABBA get called everything from plastic Euro-cheese to camp icons to straight-up pop geniuses -- so maybe there's room in there to call 'em psychedelic, too. OK, I admit that there's nothing on ABBA Gold or the Mamma Mia! soundtrack that remotely approaches the same area code as even the poppiest moments from Pink Floyd, much less the full-fledged acid-rock freakouts of, f'rinstance, Hawkwind. But there's an interesting oddity that kicks off their 1977 release ABBA - The Album (not to be confused with 1975's ABBA, which is apparently just an album). "Eagle" is a slow, synthesizer-heavy ballad with lyrics about some sort of mysterious astral-travelling international (or interstellar) visitors and the mystical socialization opportunities that arise therein, and it's so out of place in their more familiar peppy and upbeat ouevre that I'm a bit surprised it turned out so well.
And in case you think that stretches the definition of "psychedelic" way too much, I gotta confess that it didn't entirely come to mind until I saw this clip. It comes from ABBA: the Movie, which is why it starts with some vague plot-related hijinx about an interviewer having a sort of awkward-looking surprise encounter with ABBA in an elevator. But in short order, that elevator ascends into some bizarre multicolored laser light show, and we move to a series of shots of a windblown Agnetha and Anni-Frid going through this 2001/Doctor Who/ABC Movie of the Week space-tunnel. It's enough to make you listen to that "flying high" bit in the chorus just a little more closely.