I’ve heard of them but I’m not familiar with them—couldn’t name a single song by any of them, nor could I picture what they look like.
I’m not Elmer J. Fudd, but I think Bow Wow Wow did “I Want Candy.”
Admittedly my list leans more towards personal favorites, but as none of these bands would be out of place in a list of greats, I think I’m ok.
I am excluding solo artists.
The Who - incredible hard rocking energy, and each member is ferocious and unique on their respective instruments. Favorite track of the moment is The Real Me.
Queen - A great mix of theatricality and rock, and I always feel like the band is kind of winking at us all the time- they never took themselves too seriously and the playfulness comes out in the songwriting and in concert footage.
Genesis - My favorite prog band and while I don’t love all eras (I personally could do without everything between Wind and Wuthering and Invisible Touch), the fact that they had 20 years of great material is a rare feat. I won’t spend too much time dissecting their greatness, but Collins, Gabriel and Banks are all unique talents and along with the other two (who also are no slouches) managed to create some weird, beautiful, and compelling music.
The Police - A unique sound and unique writing. Their approach does not sound like anyone else. Maybe an odd comparison, but unlike Genesis, their music is empty and full of space. An intriguing sound, and definitional of the era.
Jethro Tull - The only band on my list with blues roots. Their unique folk sound, Ian Anderson’s flute, voice, writing, guitar playing, and persona are all captivating.
The Beatles - ‘cause. Their greatness as the anointed progenitors of so much of modern pop music is hard to argue against.
I also want to give a runner-up position to Supertramp, who I struggle to think of as a “great” band, but they have some stellar songs over many albums, and I find their music really interesting and thoughtful.
Kate Bush
Peter Gabriel
The Beatles
The Police
Madness
Tears for Fears
Divynals (Aussie though)
Altered Images
Book of Love (American i think)
Concrete Blonde (also American and the guy sang some)
Clannad
Eurythmics
Bananarama
“Recently” there being the 80s 
Cocteau Twins. My Bloody Valentine. Lush. Slowdive. Selecta. Yazoo. Strawberry Switchblade. All About Eve. Steeleye Span. Florence and the Machine. Chvrches. Wet Leg. Big Moon. The Last Dinner Party. Curve. Silverfish. Everything But The Girl. Fairground Attraction. Katrina and the Waves. Garbage.
I could do that all day.
A band I forgot in my earlier list fronted (jointly) by a woman was The Beautiful South, they wrote some fantastic tunes and lyrics.
A succession of women, all extremely talented.
You forgot to say “OK Boomer!”
Guilty as charged. But in mitigation, may I point out that I proposed London Grammar ? 
j
As I’ve been reading this thread, I’ve been thinking “according to what metrics?”
tl;dr
If we look at how Dopers skew in demographics, there’s no surprise seeing what groups are being mentioned again and again. There’s stuff I spent way too much time listening to during the 70’s/80’s, as a teen and young adult, which I think is ‘the greatest’ but I’d have a hard time defending.
Can a band that made one outstanding album be considered the greatest, judged only on that? I mean, if we’re talking albums, then yes, but not the band in itself. One of my all time favourites is by Queen (Sheer Heart Attack), but the rest of their output is kinda only OK, in my opinion. Should they be among ‘the greatest’ then?Another way to look at it is how music history will see things. I googled “Contemporary with Mozart” and got this list:
- Muzio Clementi.
- Franz Krommer.
- Josep Haydn.
- Carl Stamitz.
- Carlos Baguer.
- Joseph Ignaz Pleyel.
- Francesco Antonio Rosetti.
- Johann Baptist Vanhal.
The only familiar name, to me, is Haydn.
Groups and music that I thought would stand the test of time are already fading. i.e. Hendrix, Doors and many others. As a comparison, how many millennials know of Errol Garner, Lionel Hampton or Benny Goodman? Without googling? Just from hearing the name?
/tl;dr
In short, outside of specific classes dedicated to music history, there’s only one group that will be studied in 200 years. And you know which*.
*Cue terrible jokes about Napoleon XIV, 1910 Fruitgum Company and such.
I don’t think Tenpole Tudor were really that good
Great post all around, thanks for sharing your thoughts.
My wife introduced me to Tull. Even though they are well regarded, I feel that they are still a bit underappreciated. Especially in their song compositions. And I do love their early work you mentioned. Their greatness is kind of stand alone. I’m not sure how much influence they exerted. Maybe because they were not well understood?
How do you reduce wind-drag on a bassist’s car?
Take the Domino’s Pizza sign off the roof
What do you throw a drowning bass player?
His Amp.
What are the three most difficult years in a bass player’s life?
Second grade.
Sorry, posted with respect and love.
Ha, love it! Female fronted bands had a lot of success in the 90s (in the UK anyway) - Catatonia, Sleeper, The Cranberries, Elastica, Garbage, Skunk Anansie - all much more my thing than the ‘rock gods’ of yore.
I was waiting for someone to include them, in the context of female leads. Annie Lennox is one of my favourite singers, just an amazing voice.
No, Frank Zappa’s eldest daughter Moon Unit Zappa just last month released a tell-all autobiography of growing up in the Zappa household called Earth to Moon. There was a certain degree of resentment and dysfunction in the Zappa household.
Just to make Silenus’ point more directly, the band was named after the entire rhythm section of Mick Fleetwood and John McVie. Fleetwood just looms larger because he eventually moved from internal mediator to actual band manager and became the de facto spokesman.
According to Trek, its…Beastie Boys right?
10,000 Maniacs, Romeo Void, Throwing Muses, Four Non-Blondes…none of which are English though, I think
The BBC have just started a poll to find the best British bands, although they have a shortlist to vote from. It’s worth a look down the list though:
Nitpick: That says “groups,” not “bands.” Which makes it more reasonable that they include vocal groups such as One Direction and the Spice Girls.