Still a cover, but I’d have to pick “Phantom Of The Opera” for them.
For Cocker I’d say You Are So Beautiful.
VH I’d pick Runnin With The Devil.
VH: Eruption in terms of the effect it had on guitar-based music and hair metal going forward. But I would say Panama for its combo of guitar pyrotechnics and crossover commercial popularity. Hot for Teacher as well.
It’s been said in nearly every post already, but Satisfaction. A Day in the Life is often listed as the best Beatles song, but it’s definitely not their signature song. As a solo artist, though, “Imagine” is indisputably John Lennon’s signature song.
Here’s a dozen bands I don’t think have been mentioned yet:
Oasis - Wonderwall
AC/DC - Highway to Hell (though a case could be made for Back in Black, Dirty Deeds, and It’s a Long Way to the Top)
Green Day - Time of Your Life
Blink-182 - All the Small Things
Beastie Boys - Intergalactic or Fight For Your Right
The Clash - Rock the Casbah
The Ramones - Blitzkrieg Bop
Sex Pistols - Anarchy in the UK
Eminem - Lose Yourself
Arctic Monkeys - I Bet You Look Good on the Dance Floor
My Chemical Romance - Teenagers
Talking Heads - The Road to Nowhere
I was going to include Kendrick Lamar with Swimming Pools, but really it’s just his breakthrough song. It’ll probably turn out to be his signature song, but it’s too early to say for sure.
Beastie Boys is Sabotage. It combines their over-the-top bombastic-ness and their cool urban groove-master rappers. That opening riff is so damn durable. It’s practically Rage Against the Machine.
The Ramones = Sedated. Maybe Rockaway Beach.
Talking Heads = so many!! I would go for Once In a Life Time (“You may find yourself…”) or Life During Wartime (“This ain’t no party!”)
Oh, come on…you simply CANNOT record a song called “Rock and Roll High School” and NOT have it immediately become your signature tune.
Sedated and Rockaway Beach are the songs that my kids shouted out from the back seat on long drives ;). When my mid-life crisis rock band played local bars, those are the songs that got folks pogo’ing. I stand by my position 
Stones? Sorry, you’re mostly all wrong!
It simply, must be, has to be, cannot be other than, Sympathy for the Devil.
You’re entitlted to your opinion, of course. But if you disagree, I think you are wrong.
Neil Young? Rock in’ In The Free World!
AC/DC → wow, tough one. Call it a 3-way tie between “Back in Black”, “Dirty Deeds” and “Heaven and Hell”.
Aerosmith → “Dream On”, or maybe “Sweet Emotion”.
Black Sabbath → another toughie. I’ll say “Black Sabbath” but could also be “Paranoid”, “Iron Man”, or even “Heaven and Hell” if you want to divide up the eras.
Green Day → “Good Riddance (Time of Your Life)” is probably the one, if only because 90% of people don’t know the real title. 
I’d personally pick “Longview” or “Jesus of Suburbia”.
Iron Maiden → “The Trooper”, with many possible alternates.
Kansas → “Dust in the Wind” barely edges out “Carry On Wayward Son”, much as I hate to admit it.
Pantera → “Cowboys from Hell”, pretty easy.
Talking Heads → gotta be “Once in a Lifetime”, hands down.
ZZ Top → I’m gonna say “Sharp Dressed Man” is a lock here.
Woah there, pilgrim. Blitzkrieg Bop?
Well, except when you’ve already written Blitzkrieg Bop.
I’ll give you this, Hot For Teacher was one of the ass-kickingest video of all time:
As for Neil Young I’d think Heart Of Gold or Needle And The Damage Done.
And in a similar vein
Umm, La Grange?
Missed the edit window…
ZZ Top - La Grange, that’s the lock.
Can’t argue your point You have the chant of BBop and the “Ba Ba Ba-Ba” end of Sedated. Both are timeless in their ability to make people go nuts. The only other song that stirred the pot as much was the opening bars to Blister in the Sun.
Here’s a tough one: Lynyrd Skynyrd. Is it “Free Bird” or “Sweet Home Alabama”?
For Talking Heads, it surely would be “One in a Lifetime,” no? I guess, for my definition of “signature song” it would be.
For The Mamas & The Papas, it’s “I Dig Rock And Roll Music”.
No, I know. But still.
No way! Monday Monday or better yet, California Dreamin’
Ooo…that’s a real tough one. The latter certainly gets more play and I suspect is more widely known than the former, but “Freebird” is kind of like “Stairway” in terms of rock’s iconic songs. I think “Sweet Home Alabama” better reflects the sound and style of Skynyrd, but “Freebird” is so legendary, that I’ll go with that for Lynyrd Skynyrd.
ETA: And, of course, that’s “Once in A Lifetime” not “One in a Lifetime” a few posts back.
Word, man! California Deamin’ all the way!!!