That was my first thought.
Actually, an excellent choice. As is Genesis’ “Invisible Touch,” which someone else mentioned. (I don’t care for the song much, but it’s as 80s as they come.)
I always think of Video Killed The Radio Star as the most 80’s song, but I think it came out in 79.
Just googling around, I found “Blue Monday” by New Order, which I never heard of, and WOW that is REALLY essence of the 80’s. It’s got that cold minor key drum machine/synthesizer and a thunk thunk thunk dance beat.
Fools! You are like listless monkeys carelessly flinging your poop. You need to back up your assertions with science and logic! 
And this question has been answered:
http://boards.straightdope.com/sdmb/showthread.php?t=485990&highlight=Warrior
“Don’t You Want Me,” as mentioned upthread
And the other one is the answer to a joke: what’s worse than sweat on Olivia Newton John?
Come On Eileen
On a different note, I find it interesting that arguably the biggest band of the 80’s, U2, does not have a 80’s sound.
I’d nominate “The Final Countdown” by Europe
Hah! I have no recollection of that thread, but it looks like I agreed with the mention of “Melt With You,” as well as “Don’t You Forget About Me” and " Take On Me," so I guess I’m at least consistent, after six years and nearly a week to the date.
And apparently I had better music tastes. Depending on your appreciation for Spandau Ballet, of course.
Not really a matter of taste, but I’d personally say that “Gold” (or “True”) and “Bizarre Love Triangle” (New Order) are more of what I think of when I think of the 80s than Tiffany. Or how about Debbie Gibson?
No one’s mentioned a song by Asia yet?
Heat of the moment, Sole Survivor, or Only time will tell, it doesn’t really matter which.
Jessie’s Girl.
My wife says Material Girl
I was thinking West End Girls
Wouldn’t be upset if Don’t You (Forget About Me) took the crown in this scientific poll
Michael Jackson, Madonna, Prince and Phil Collins basically dominated the decade.
“1999” has it all: it’s a synth-heavy Prince song about Cold War paranoia, and it was essentially ripped off by Collins as “Sussudio”. Those factors alone should rank it pretty high.
But does it make your blood run cold? As if your memory has just been sold?
My angel is the centerfold. ANGEL IS THE CENTERFOLD!
Gold by Spandau Ballet.
The most 80s song must have:
Synthesisers
Saxophone
Lyrics that sound deep and poetic but upon analysis actually mean nothing
The band must have:
Ambiguously gendered members
Big hair and shoulder pads
Too much make-up
The video must have:
Fans blowing said big hair
Lots of draped cloth
On a stage with a crowd
Soft focus
So something halfway between Europe’s Superstitious and Bonnie Tyler’s Holding Out For A Hero.
That was my first thought too.
LOVED that video. Later at Christmas (and ever since) I sing, “Going shoppin’… from A to Z…”