The 1980s gave us a wide variety of excellent music. The new wave on the radio of the early 80s slowly turned into more hair metal bands later in the decade. But many of the great bands in the early '80s didn't stop making excellent music.
And because the music was so diverse early in the decade, the music-listening public could quickly move their fandom from one band to the next. This meant some worthy bands got left behind more quickly.
But the three bands that follow are ones that not only should people have kept listening to for the entire decade, but should keep having on high rotation. Multiple records with multiple great tracks? Yes, these bands have that and more.
Front 242
You can't listen to Front 242 without hearing rumblings of Nine Inch Nails. But that's likely because Trent Reznor of NIN would have been influenced by Front 242. The song "Welcome to Paradise," in fact, seems like a more primitive recording of a very early NIN track. But that's not meant as a slight to Front 242; They just didn't have the same tech that Reznor would in later years.
Front 242 began in Belgium in the 1981 and basically helped create techno and industrial music. The band called it "electronic body music." The bands they helped influence are simply too many to name, but it's important to note that Front 242 were more influenced by groups like Joy Division, so you get an idea of how Front 242's sound, while electronic, also can have dark undertones. Think of something like Depeche Mode's Black Celebration album and you'll somewhat get the idea.
If you like groups such as Ministry, you'll love Front 242. The lyrics aren't overly happy, and that's part of the point. But early Front 242 concerts were more like metal concerts with the volume turned up to 11 and a stage presence that was highly aggressive. In other words, you should find and watch a bunch of Front 242 videos on YouTube because it will make your day better.