Journey
Journey is one of the catchiest bands ever, but they're also the most annoying for the same reason. Despite being such a popular band from the 1980s, how many songs of theirs can you actually name? Most people just know "Don't Stop Believin'," which is a shame.
Asia
The song "Heat of the Moment" is pretty much Asia's only hit, and no one really plays that song unless you're at a party or building a 1980s-specific playlist. What happened to Asia after that song? No one really knows, or cares.