I've always thought Keith Richards' Main Offender was an overlooked gem.  It's a beautiful, smooth-but-complicated mix, disguised as simple Stonesy rock.
 
James' Laid album was also a masterpiece (Eno), overlooked by the single.

Here's another example of genius simplicity...great arrangement, vocals, and a kind of chord progression we don't hear in pop music anymore.
 

 
Not directly related, but on the topic of bands that sound like the Beatles (also a truly great pop song)...
 

 

Special birthday edition
Old Wild Men

Ginger Geezer

Tame Impala really nails the poppy feel for me: https://youtu.be/sBzrzS1Ag_g (Song starts at 1:18)
Maybe some Caribou: https://youtu.be/PNbuMeK3f58 

Though I'm more into this (if King Krimson makes the list, lol)

The Mars Volta https://youtu.be/fE6YN9VcPPA 

scook - agree with Viv Stanshall.  I still see Neil Innes from time to time with incarnations of the Bonzos, or the Rutles which often includes Eliott Randall. They actually rock well in their own right!
We should point out the above video of Viv S is Cockney rhyming slang and actually makes sense!
 
 
 
 

I was going to mention Neil Innes earlier but yeah aside from the the aforementioned associations here is one with the other McCartney

It's easy to get turned off by bands that became massively popular and sold millions upon millions of records, but...all of Queen's albums during the 70's just blew me away, and not because they were popular, but because they were doing something that I never heard before.  Brian May's guitar orchestrations and Freddie Mercury's vocal arrangements on top of that massive rhythm section was unique enough to get me hooked right from their first release.

RobWS
It's easy to get turned off by bands that became massively popular and sold millions upon millions of records, but...all of Queen's albums during the 70's just blew me away, and not because they were popular, but because they were doing something that I never heard before.  Brian May's guitar orchestrations and Freddie Mercury's vocal arrangements on top of that massive rhythm section was unique enough to get me hooked right from their first release.

this  ^^^

The good stuff stands up over time, regardless of initial popularity. "Legs", that's what they call it in the movie business to describe a film that opens weak but gradually builds an audience. They say it "has legs".
 
Ashlee Simpson's "Autobiography" went platinum in 2004, but who's listening to it today? Nobody, I suspect.
 
"Pet Sounds", OTOH, barely made a blip on the charts on its release and was widely dismissed by critics. But it changed pop music forever, influenced every record producer since, and makes every Top N list of the greatest albums of all time.

I think these guys got "legs"

or is this what is meant by "legs"