It should be something with some cheesy wheezy synth and a cheap looking video, even though by the mid-late 80’s labels were doing some big-budget videos.
There’s a lot of songs that would fit that equally well, most already mentioned here, but since the 80’s were all about MTV, I’d go with Video Killed The Radio Star, for obvious reasons.
I heard this piece of 80’s “Gold” recently: Warrior Official Video - Mark Foster, A-Trak, and Kimbra - YouTube
Released May, 2012! Goddammit, I hope this isn’t a trend.
I do remember hearing Golden Brown by The Stranglers although I would consider it a very minor hit if anything. It’s an odd choice, in 3/4 time with a harpsichord…hardly characteristic of 80s music to me. But if it works for the OP…
For me the 80s don’t really get going until certain technical aspects of studio sound are firmly in place. This means gated drums and/or chintzy drum machines, digital reverb, certain digital synths like the DX7 and the discarding of warm midrange-y guitars in favor of digital sounding distortion or clean chorus guitars. The combination of these things don’t really come into full swing until about 1985 or so. When you have an established rocker like Tom Petty using a drum machine on “Don’t Come Around Here No More”, it’s a sign of the times. Robert Plant transitioned from a Zep sound on Pictures At Eleven (1982) until he gets into full 80s (depeche) mode on Shaken’n’Stirred (1985)…with Principle of Moments as an in-between stage. Then there’s the Peter Gabriel’s manifesto of 1985, So.
Anyways, Take On Me and Don’t You Forget About Me are pretty definitive to me.
I agree Lemur866 has come up with the best answer for both the 80s and 90s.
This. As much as any one song could be chosen.
I say Shakedown is a quintessential 80s song - slick corporate rock with synths, horns and dopey macho lyrics, used as the soundtrack for a Tony Scott movie.
Wang Chung - “Everybody Have Fun Tonight”
It’s bizarre, bouncy, shallow, superficial, and still to this day nobody knows what the hell it means. Just like the 80s.
Take On Me gets my vote because it sounds undeniably 80’s and has a really amazing music video that stands up even today while still looking very 80’s.
I would like to nominate The Final Countdown just for the wheezy synth that epitomizes so much 80’s music.
My dad used to watch SNL just to see this. 
I second the vote for Take on Me, but I’d like to offer Van Halen’s Jump for consideration. Heavy on guitar, light on lyrics.
David Lee Roth said the song is about suicide, but he’s mistaken. It’s about Eddie Van Halen showing what a kickass guitarist he is.
Exactly what I opened the thread to say.
In the 80’s I couldn’t stand the popular music of the day. However, I was a teenager then, and you know how music puts a thumbtack on the corkboard of time…
Borderline by Madonna. The very opening notes of the song bring me to 1984, or whatever year it was.
(Luckily, Ian Gillan had 2 records out then that saw me through the 80’s: Born Again with Black Sabbath, and Perfect Strangers, the Deep Purple reunion record.)
“Total Eclipse of the Heart” then?
“Don’t You Forget About Me” is good, but for me the ultimate 80’s song will always be “I Melt With You” by Modern English.
I was thinking of that one, too, yet somehow forgot to mention it. I think “Don’t You Forget About Me” is probably gonna beat it out for me, but “I Melt With You” is a serious contender, as well as a-ha’s “Take On Me.”
Several months after VH’s “Jump” was #1 in the States, the Scottish acoustic-folk band Aztec Camera remade it. Don’t believe me? Here it is.
I know that cover. Didn’t realize it was that soon after the original.
Van Halen isn’t a bad one, either. My early 80s memories are certainly full of “Jump,” but that’s because I was (and still, unfortunately, am) a Cubs fan, and back then, it was pretty much their theme song during WGN broadcasts.
I still think Huey Lewis could figure into this. Nobody, and I mean nobody, is trying to imitate that sound now. It is soooooo stuck in the 80s. While my other choices, Simple Minds, a-ha, Modern English, I could actually see working out for a current band, even if they are simply preying on 80s nostalgia.
Because nothing epitomizes the 80s like a Van Morrison/They Might Be Giants hybrid?
The problem with “Don’t You Forget About Me” is that it doesn’t make me think “80s!!”, it makes me think “The Breakfast Club!!”
Does anyone really picture the 80s when they hear it? Does anyone even remember the video? Or do you just picture Judd Nelson walking across the football field doing a freeze frame fist pump?