Lots of great choices here, but I’ve got to give love to:
“Don’t You Want Me?” Human League
“Head Over Heels” Tears for Fears
…and, what I consider to be the Most 80’s Song Ever, “Wild Wild West,” Escape Club. 
It’s got fake-Jamaican rapping; shout-outs to safe sex, valium, and big hair; an actual LINE about “livin’ in the eighties;” and lots of kooky synth sound effects thrown in for good measure.
Anything by The Police, my personal 80’s band, but especially:
Every Little Thing She Does Is Magic
Roxanne
Omegaman
So Lonely
Three guys made all that noise. The best. Ever.
Kyrie Eleison - Duran Duran
Amanda - Boston
Here I Go Again - Whitesnake
Take My Breath Away - Berlin
Danger Zone; Footloose- Kenny Loggins
Almost everything on the “Heart” album - Heart
I was going to suggest the ultimate rock song, Boston’s “More than a Feeling” but that’s from the 70s. So, I’m going to with The Cars’ Drive.
Wow, a lot of good ones.
For pop
A second on “West End Girls” and “Careless whispers”, and a bunch of others
Electronic - “Disappointed”
Bananarama - “Cruel Summer”
OMD - “Dreaming”
Double - “Captain of her heart”
Kenny G & Kashif - “Love on the rise”
Miami Sound Machine - “Rhythm is gonna get you”
Pointer Sisters - “I’m so excited”
Stacy Q - “Two of hearts”
Lionel Richie - "Love will conquer all
Paul Davis - “Cool night”
Debarge - “Rhythm of the night”
For pop rock
Benjamin Orr - “Stay the night”
Philip Bailey & Phil Collins - “Easy Lover”
Lionel Richie - “Running with the night”
Kim Wilde - “You keep me hanging on”
Joe Lynn Turner - “Endlessly”
Edit - Took out three songs that were form the 90’s (because I didn’t read the title close enough)
Okay, this time you beat me…guess what I came in here for?! 
Behind the Wall of Sleep - Smithereens
Boys of Summer - Don Henley
Breakup Song - Greg Kihn
Can’t Stand Losing You - The Police
Come Dancing - The Kinks
Erotic City - Prince
Going Down to Liverpool - The Bangles
Heartbeat City - The Cars
In Your Wildest Dreams - Moody Blues
It’s Different for Girls - Joe Jackson
Kids in America - Kim Wilde
The Lady Don’t Mind - Talking Heads
Lovers in a Dangerous Time - Bruce Cockburn
Maneater - Hall and Oates
A Matter of Trust - Billy Joel
The Metro - Berlin
A Million Miles Away - The Plimsouls
No Myth - Michael Penn
She Bop -Cindy Lauper
Southern Cross - CS&N
Spanish Bombs - The Clash
Subdivisons - Rush
Summer of 69 - Bryan Adams
They Don’t Know - Tracy Ullman
All of Van Halen’s stuff before the new guy showed up. Educate yerself: “Panama” is a good place to start.
The Outfield - Your Love
I mentioned in a recent thread that I had “Heart And Soul” by T’Pau earwormed into my brain for about three months the year it came out. 
Another song that totally stuck in my head for an extended period of time was “Head To Toe” by Lisa Lisa and Cult Jam.
Actually, “Kyrie” was done by Mr. Mister and was their most obviously Christian rock tune.
Humorous aside which I was reminded of by your list: “Still Of The Night” by Whitesnake immediately precedes “Stonehenge” by Spinal Tap on an 80s mix I have on my iTunes. I defy anyone to identify which song was done by a bunch of comedians and which was done by a real band.
Alice Cooper?
As far as I know, that atrocity came out in 1998 and was not a remake.
Mr. Mister, Duran Duran, Lisa Lisa. Fine, fine. Were they all from Walla Walla?
They were all members of the Tom Tom Club.
New Order - “True Faith” (one of the finest pop songs of the last 100 years)
the Human League - “being boiled” and “keep feeling fascination”
Visage - “The damned don’t cry” and “Fade to grey”
Altered Images - “bring me closer”
the Smiths - “this charming man” (my vote for finest pop song of all time, period)
You are correct, sir. That has a great lyric “I want to hurt you just to hear you screaming my name”
The best pop song of the 80s was “Home Sweet Home” by motley crue
Incorrect, the best song was “Every Rose Has Its Thorn”, even though it wasn’t particularly 80’s. When I think 80’s I think something like “Safety Dance.”
No mention yet of INXS - Never Tear Us Apart or What You Need.
Also, Def Leppard - Photograph.
I remember a lot of 60s and 70s groups and individual singers made comeback singles in the 80s: Beach Boys, Starship, Fleetwood Mac, Siouxsie and the Banshees, the Who, Paul McCartney, Robert Plant, Steve Winwood, and so on.
Which reminds me: whatever happened to The The?