In my teens and early 20s, I was primarily into what was then defined as "hard rock" and/or "heavy metal." But my two main developing "sub-interests" where I liked a few bands here and there, often because of friends who were more heavily into those genres/subgenres were new wave and thrash.
I recognize that, as with many genres and subgenres, we could spend the entire thread arguing about what does or does not qualify as "new wave." Personally, I don't really care to have that debate (although it's Kev's thread, and if he intended that, then by all means have at it) and bash people's band choices, unless they are WAY outside the accepted boundaries of what could fit. I enjoyed quite a few new wave bands. But there are only a small number that I actively followed and bought their albums:
-Depeche Mode: Perhaps the "kings" of new wave? They were HUGE when I was in high school. And simultaneously, somewhat underground except for those in the know. In the U.S.--at least my corner of it--it seemed like they were one of the first to come out of and embrace both the punk roots and pop influence and gain a massive underground following that grew and grew until they were too large to ignore. My best friend at the time was REALLY into them, so I was familiar with songs here and there from their early stuff. But what really got me into them was Music for the Masses. I believe that was my first purchase, and then I went back and got the back catalog. I thought 101 was fantastic as well. Great performance, and really functioned well as a nice hits package that dove nicely into the back catalog. Violator was pretty good as well (really nice driving album for a lot of road trips up and down I-95). But I lost interest after that.
-Siouxsie & the Banshees: LOVED this group. I remember seeing them live at the Greek Theater in Berkeley in 1987, with Andy Sommers and Julian Cope opening, and was blown away by her and her band. Oddly, Through the Looking Glass was and is my favorite album from them. I say "oddly" because, for those who don't know, it is a covers album. But if you didn't know the songs (and there is a good chance one may not, since they are mostly pretty obscure. But what a great job! Tinderbox is also a really great, fun album. Cities in Dust is a great original from them during that era. Oddly, before Peepshow came out in--what was it, '89?--other than Cities in Dust, I think that in the U.S., they were best known for their covers of the Beatles' Dear Prudence and Helter Skelter. Anyway, fantastic band.
-U2: They round out my "top 3." I guess nowadays, it is easier to just count them as a "pop" band, since that is where they evolved to. But early U2 was considered by most to be "new wave" for sure. I didn't really get into them heavily until Joshua Tree. Perfect album as far as I'm concerned. One of the best all time from anybody. The back catalog is really good as well. But after that, they were hit and miss, and I basically stopped following them in the mid-'90s.
-Honorable mention to Cory Hart, if he counts as new wave. Boy in the Box was a great album.
Others I enjoyed, but did not follow as closely include Blondie, Devo, and Talking Heads. But there was a lot of good music in this genre.
Taking the conversation off on a bit of a related tangent: By the early '00s, I had mostly all but forgotten about new wave. But right in that timeframe, I discovered this at-the-time somewhat-obscure goth metal band from Italy called Lacuna Coil, upon a recommendation from a guy on the Y&T/Dave Meniketti forums. What immediately struck me about the album Comalies was how it took goth/new wave synthesizers and vocal stylings and paired them with modern metal. That sound was right up my alley at the time, and I loved it. I remember mentioning to Samsara at one point in time that I loved how they sounded like a melding of '80s new wave with modern metal, and he VIGOROUSLY shot down the mere suggestion that there was anything "new wave" about them.
But I still hold to that. I clearly hear that influence, and it's no secret that the band was influenced heavily by bands like Depeche Mode, Duran Duran, and the Chili Peppers, so they definitely have that punk/pop, new wave melding stable of bands in their influences, and I hear that come through in their style.