I will explain my choices as to why these particular songs I consider to be their quintessential, or most representative of their body of work.
The Rolling Stones - Jumping Jack Flash. Why? Because it is essentially a riff-based song that was a variation on rock forms already established by other groups. This is what the Stones did. However, the Stones managed to do it just a little better. Keith Richards catchy guitar riff - as it so often happened - managed to make this a perfectly hummable tune that you could walk away from whistling the tune and feeling good.
Queen - Bohemian Rhapsody. This one happens to be not only their most quintessential but also one of their very best. Why? It features the complex vocal harmonies, and complex time signature changes we so closely associate with this group
The Who - My Generation. No, unlike Queen this is probably not their best song but it contains all the elements we associate musically with The Who, and most importantly the lyrics of this song represent youth rebellion, which really is what a lot of folks think of when they hear The Who.
The Beatles - Sergeant Pepper’s Lonely Hearts Club Band. Where to begin? Well, it represents an essential piece of psychodelia and will forever be associated with both the decade of the 1960’s and the Beatles band. Seriously, I would submit that this song will be remembered in connection with the Beatles centuries from now much as we might think of Toccata and Fugue in connection with J. S. Bach. They had that kind of cultural impact and Sgt Pepper probably represents the pinnacle of that cultural influence.
I like Honky Tonk Women for the Stones. That’s them in a nutshell.
I don’t know anything about Queen.
I stopped being a Who fan after The Who Sell Out, which is when they lost their sense of humor. I’ll go with Happy Jack, as being best representative of that early period.
Kind of an off-the-wall pick for the Beatles: The Two of Us. Because it’s really John and Paul together, which they hadn’t done much of since at least Rubber Soul.
Yeah, I may have to change my choice. Something like “Honky Tonk Women” might do better. I’m not sure “Sympathy” is particularly representative – that one seems to stick out a bit from their barroom country-and-blues-rock band sound.
I like this analysis. I too interpreted the OP as asking for the song that contained all the essential elements of a band’s work product. I thought Won’t Get Fooled Again had em, but I forgot about that “quasi bridge/chorus” that is Townshend’s signature. I’ve been a Who fan from way back. Who’s Next was the first album I bought. I was 14 and it was over a decade after it was released. Taking nothing away from Daltry, Townshend’s vocals, although deployed less, have always equally distinguished the band. (However Much I Booze, you can’t sing better than that.) I remember when It’s Hard came out. Reviews were mixed. Part of one review that has always stuck in my mind said something like, about the track Athena, when Townshend delivers the lyrics “Just a girl, just a girl”, true fans will be in Who heaven. I was. And when I played the record for the first time, that being the first track, whatever came next didn’t really matter.
It was just less than 5 years later that they last performed together on the rooftop in London. To cop the title of a Who song, what an amazing journey it was.
Dear Prudence may just be my alltime favorite Beatles song. I particularly like the drumming in the last verse…and I only recently found out that it was Paul playing drums. It was the day Ringo quit the band.
Queen: Dunno, “Bohemian Rhapsody,” I guess? (Not sure this one is all that representative, but I don’t actually know / like enough Queen songs to have any better ideas.)