While it's probably easy to throw Falco into the one-hit wonder category, he had at least 3 or 4 top 20 hits in the US and I think more songs than that in the Top 10 in several European countries. RMA hit #1 all over the world, which is why it's understandable to throw him in this category.
Hits that I remember:
Rock Me Amadeus
Der Kommisar (which I think was a bigger hit when covered by "After the Fire" a year or two later)
The Sound of Muzik (sp?)
Was never into 80s 'music' at the time it was happening although in retrospect some musical things from the 80s were 'not bad' to listen to. I always liked the Phil Collins & Phil Bailey hit Easy Lover from 1985 and also Tears For Fears- Everybody Wants To Rule The World,Shout & Sowing The Seeds Of Love were all pretty good 'pop' songs to listen to.