What I am looking for is the one song from each of the following seven groups that best define/represent those groups for you. No substitutions or additions to the groups, and only one song per group. The groups(and my choices) are:
The Beach Boys-All Summer Long
The Beatles-Love me Do
The Rolling Stones-Sympathy For The Devil
The Who-Who Are You
Pink Floyd-Childhood’s End
Queen-Crazy Little Thing Called Love
The Doors-Riders On The Storm
The Beach Boys-Wouldn’t It Be Nice
The Beatles-I Saw Her Standing There
The Rolling Stones-Sympathy For The Devil
The Who-Baba O’Riley
Pink Floyd-Wish You Were Here
Queen-Bohemian Rhapsody
The Doors-Roadhouse Blues
My picks might be different tomorrow, but as of this moment:
The Beach Boys-Help Me Rhonda
The Beatles-Revolution
The Rolling Stones-Get Off Of My Cloud (El Macambo version)
The Who-It’s Not Enough
Pink Floyd-Echoes
Queen-Keep Yourself Alive
The Doors-Close To You (Absolutely Live version)
Beatles: Abbey Road Medley (if that’s cheating, then Come Together)
Bonzo Dog Band: Humanoid Boogie
Pink Floyd: Summer '68
Grateful Dead: Uncle John’s Band
Queen: '39
The Who: I Can See for Miles
Kinks: Lola
Well, you got four of them-what about the other three?
Beach Boys: Good Vibrations
Beatles: A Day in the Life
Rolling Stones: Gimme Shelter
The Who: Who Are You
Pink Floyd: Shine on You Crazy Diamond (1-5)
Queen: Killer Queen
The Doors: Riders on the Storm
That being said, the Doors suck out loud and it’s an insult to the other six bands to include them.
That being said, there are no seven bands on earth where someone wouldn’t say the same thing about one of them.
But my opinions are more important than theirs!
Knock it off, or the next list will have The Hudson Brothers. 
Beach Boys: California Girls
Beatles: Twist and Shout
Rolling Stones: Jumpin’ Jack Flash
The Who: Eminence Front
Pink Floyd: Comfortably Numb
Queen: Stone Cold Crazy
The Doors: Not To Touch The Earth
Beach Boys: Surfing Safari
Beatles: Norwegian Wood
Stones: Rocks Off
Who: Substitute
Pink Floyd: Time
Queen: Somebody to Love
Doors: Peace Frog
The Beach Boys- God Only Knows
The Beatles- A Day in the Life
The Rolling Stones- Gimme Shelter
The Who- Baba O’Riley
Pink Floyd- See Emily Play
Queen- Under Pressure (if that doesn’t count 'cause it’s with David Bowie, then “Somebody To Love”)
The Doors- Break On Through
I feel that way about Pink Floyd and The Doors, but I like both songs I picked from those bands.
The Beach Boys-Good Vibrations
The Beatles-Eleanor Rigby
The Rolling Stones-Satisfaction
The Who-Won’t Get Fooled Again
Pink Floyd- Wish You Were Here
Queen- Killer Queen
The Doors- Break On Through
These are my choices for “Most Representative”, not necessarily my favorites.
The Beach Boys-Wouldn’t it Be Nice
The Beatles-Can’t choose
The Rolling Stones-Paint it Black
The Who-Baba O’Riley
Pink Floyd-Wish You Were Here
Queen-Don’t Stop Me Now
The Doors-LA Woman
The Beach Boys - Little Deuce Coupe
The Beatles - A Day In The Life
The Rolling Stones - Satisfaction
The Who - Won’t Get Fooled Again
Pink Floyd - Comfortably Numb
Queen - Bohemian Rhapsody
The Doors - Light My Fire
The Beach Boys-God Only Knows
The Beatles-Tomorrow Never Knows
The Rolling Stones-Gimme Shelter
The Who-Who Are You
Pink Floyd-Comfortably Numb
Queen-Under Pressure
The Doors-Break On Through
The Beach Boys-Kokomo (for the harmonies)
The Beatles-Norwegian Wood
The Rolling Stones-Under My Thumb
The Who-Who Are You
Pink Floyd-Another Brick in The Wall
Queen-Who Wants To Live Forever
The Doors-Break On Through
The Beach Boys - Good Vibrations
The Beates - A Day In The Life
The Rolling Stones - Sympathy for the Devil
The Who - Won’t Get Fooled Again
Pink Floyd - Wish You Were Here
Queen - Under Pressure / Somebody To Love (depending on if UP counts)
The Doors - Break On Through
Judge’s Ruling-If it appears on a Queen album, it counts.