I liked the 70s thread, where you requested one album per artist only. I'm settling on a single album per artist, but including honorable mentions (i.e., cheating).
The 80s was my biggest period of new music consumption. I'm a sucker for top 40 music from the era -- the good, the bad, and the ugly.
In no particular order:
Duran Duran -- Rio
U2 -- The Unforgettable Fire (The Joshua Tree is likely the stronger album, but hearing the opening track on The Unforgettable Fire for the first time was reminiscent of my first spin of Rubber Soul -- love at first listen). U2 was by far my favorite 80s band. I lost the plot in the 90s.
R.E.M. -- Fables of the Reconstruction (hard to overlook most every other 80s album in their catalogue)
The Cure -- The Head on the Door (HM: Disintegration and Kiss Me, Kiss Me, Kiss Me)
Guns N Roses -- Appetite for Destruction (I prefered "Lies", but it's an ep)
The Smiths -- Strangeways, Here We Come
The Pogues -- Peace and Love (more so then than now)
INXS -- The Swing (HM: Listen Like Thieves)
The Grapes of Wrath -- Treehouse
The Northern Pikes -- Secrets of the Alibi
HM: Paul Simon (Graceland), John Lennon (Double Fantasy), The Police (Synchronicity), Rush (Exit Stage Left)
...fighting urge to list hair metal albums....