For me, a lot of New Wave is of a time, and really only resonates because of the emergence of MTV and seeing the videos over and over (Human League comes to mind).
But for me, The Cars, Duran Duran, and Squeeze have, like all great bands, transcended their humble beginnings. Duran Duran was on "Later... With Jools Holland" not long ago, and turned in an explosive rendition of "Wild Boys"; they were on FIRE. I just saw Squeeze on Friday night, front row, and they were solid as a rock. Two hours, knew every song but two (to be fair, I've HEARD them, but they were from the latest two albums and so can't be called "greats" or "hits" yet) and was clapping along like a jackass for most of it. The thing was, FOR ME, the genre was so tied to video - the visual - and the music so austere, that the musicianship was often lost. The DD example shows them to be a really good BAND, and particularly John Taylor and Simon, very good if not excellent performers at their instrument. Seeing Squeeze, I was blown away by how good Glenn Tillbrook is as a musician. He sang and played lead guitar on every song, and some - Tempted was one, In Quintessence another - it was just him and a guitar playing. At one point, he did this really fast riff across the entire neck, and I was like "I couldn't play that with a year's practice!" and not only did he repeat it flawlessly, he stepped up to the mic and sang the first verse while repeating it. Listening to the simple repetition of something like "Goodbye Girl" or "Take Me I'm Yours", you'd be pleasantly surprised at the musicianship that is behind what we think of as simple and catchy songs.