What about Alanis Morissette? She went from disco-pop Debbie Gibson ripoff to the angst ridden, dictionary-less rocker we know today.
I’m gotta go with Pink Floyd. Look the word progressive up in the dictionary and there they are. They’ve done just about everything, including serious electronic and orchestral experimentation. You can divide Floyd into at least five distinct stages.
MR
How about Van Morrison? Look at the differences between Them and his solo work.
Shucks I got beaten to Fleetwood Mac.
How about Ray Charles, he has changed his style and bewildered the purists plenty.
Police - started out as a punk band (but not a very convincing one) and changed to, well their own style I guess.
Kylie Minogue - Has an image makeover every couple of months
Lovin spoonful - They were a regular uptempo pop chart act and changed to slowies.
Robbie Williams - Started off with boy band Boyzone and went solo to become the yoof culture 'serious’type - still shite though.
George Micheal - Started of as hearthrob in Wham and went solo(until he needed a hand 
) as a moody arty grown up type.
Sheryl Crow - Completely unrecognisable from her days touring with Micheal Jackson.
David Bowie - Where to begin…
Ricky Nelson - His song Garden Party was inspired by the fact that he’d changed style so much that no-one recognised him when he turned up for a golden oldies gig.
Roxy Music - changed from leading edge experimental stuff to disco ballads.
Graham Nash - Started out with the Hollies ended up in Crosby Stills and Nash.
Elvis - Oh give over - everyone knows.
Elvis Costello - Started off as New Wave went indie then country now he does what he wants.
Tom Jones - From balladeer to indie almost
Anyone who has been around a while must change or develop themselves so really you would have to count them out, to me the ones whose changes have been either sudden or dramatic as to be disconcerting aught to be the only ones named.
I was thinking “You’ve got to Work for Love” and “Just one Fix” but, yeah, no question.
Well I’d have to go with Golden Earring. They’ve been around since the mid 60s and sounded like a Beatles rip-off to a degree. then through the 70s they had a very progressive type era. then the 80s had a bunch of “pop” type songs. Then in 99 they had a hark and heavy rocking album that I never would have expected from them.
Next would have to be Iron Maiden, they started out just straight NWOBHM to a synth on Somewhere in Time then very deep dark lyrics and music on X Factor, and a progressive style on the newest Brave New World. although Maiden has always been at least somewhat progressive.
I’d also go with Rush, Black Sabbath, Gary Moore who’s done everything from Jazz/Rock fusion, to Hard Rock to blues.
I first thought of Elvis. When you listen to him singing in his eary days, he’s actually singing, instead of warbling in a hunk-a, hunk-a wa-wa-wa kind of way. He’s no musical group, but maybe that allowed him to change even easier.
I also gotta say U2. I mean they started out as Christian rock for the most part. Then they became activists for every cause under the sun. Then they became scathing commentators on politics and the pop industry. Now they’re…ah…I dunno, even I quit paying attention.
Metallica, they have changed quite a bit from their old days, some say for the better, most say for the worse.
Van Halen. IMHO, they underwent SERIOUS change.
Smashing Pumkpkins kinda evolved with every album they made, think “Zero” with “Perfect”
I suppose, but aside from singers, VH hasn’t changed all that much. A few albums they tried some different stuff. But their groove has remained much the same since 79’.
How about Pat Boone: from very popular pop singer (by singing song written by Blacks) to a leather-wearing heavy metal artist. Now, how extreme is that?
About Jefferson Airship ::d&r:: …
Don’t forget the classic ‘Blows against the empire’, labeled as Starship but definately Airplane (& Dead/Quicksilver et.al.) material. And although labeled as a Crosby solo album, ‘If I could only remember my name’ is a sequal to BATE. That being said, later JS sucked compared to JA.
And Fleetwood Mac was a blues band prior to the Bare Trees era, though with few of the long time members. I’ve got an old album stashed somewhere but I can’t recall the name.
How about Alanis Morrissette? Talk about re-inventing yourself. She went from a bubble-gum pop star a la Debbie Gibson into an angry, moody singer in the space of three years.
Well, for a lot of people my age (Move over, you geezers :D)…The Suicide Machines has changed from being a punk/ska core band (They’ve been compared to Operation Ivy) to being a namd that plays some weird slow music. Completely different focus on lyric style too. I know they aren’t a very popular band outside of the younger circles, but it’s significant to me.