Big fan of this style of music.
Echo & The Bunnymen above all (my other true musical heroes are all in the metal or goth tag, except if you would consider Sophya to be borderline newwave... i'd rather call it dream pop)
Love Bauhaus too, not just their hits but also some lesser known material. Passion of Lovers, Hollow Hills, Slice of life, All we ever wanted was Everything, Burning from the inside, ... not as famous as Double Dare, Dark Entries, She's in Parties, Bela Lugosi's dead, but certainly as good. The intro of Burning from the Inside is a masterpiece in this style of music.
Love Soft Cell too. The whole Non-stop Erotic Cabaret: close your eyes and you dream off to the sleezy alleys of the Soho area with its brothels. The album creates a dark, somewhat "must stay hidden" atmosphere and Marc Almond's vocals are fitting perfectly. Ironically I find "Youth" their best song, while it is probably one of the most antitypical Soft Cell songs. They also had great music videos.
Also like some songs by Siouxsie (I find her less known songs often to be better than her hits. Best songs: Hong Kong Garden, Red light, Rhapsody, Face to Face, Israel, Spellbound, ... songs like Red Light are very dark but not very well known, Rhapsody --where she displays her vocal reach to full extent-- was never even a single release)
Some songs by Joy Division (mainly Day Of The Lords, and Disorder)
Some songs by The Cure (especially Charlotte Sometimes, Lovesong, Fascination Street, The Hanging Gardens, and in a guilty pleasure way Why Can't I Be You)
"Marian" and "Alice" by Sisters of Mercy (whom I dislike in general, these two songs being the exception)
Also love Indochine, they were the first French language new wave act but in that era French music was mainly traditional chanson, no alternative music. Indochine paved the path for many to follow, they introduced the French audience to alternative music in their own language. Prior to them, all alternative music had to come from abroad and was sung in mainly English.
Also worth to check out are Belgian goth/newwave outfit The Breath of Life (the ONLY Belgian band in this genre of music who did not cease to exist relatively soon after their first recordings) and Israeli newwave band HaMachshefot (חמַחשֵׁפוֹת)
A gem whose records are worth a lot due to being so rare: Chinese all-female new wave/gothic band Cobra. Except for some footage on YouTube filmed with an amateur camera and some CDs that were smuggled out of the country to Germany, little is documented about them. The government didn't authorise them so they had to perform in small hidden venues, still managed to release an entire album.
German all-female (initially) band X-Mal Deutschland is very good, check songs such as "Polarlicht", "Orient", ...
I don't know if you'd count them as newwave, neofolk or gothic, it's a hard to categorise band... but Russian band Moon Far Away is brilliant too. Pity their records are hard to get outside of Russia.
Not sure if you'd consider Kirlian Camera to be new wave? Virgin Prunes are another borderline case.
Also, don't forget Nick Cave in his Birthday Party era.
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Do what Thou wilt shal be the whole of the Law.
Love is the Law, Love under Will. And...
every man and every woman is a star
(excerpt from The Book of the Law - Aleister Crowley)
"Od lo avda tikvateinu" (excerpt from the Israeli hymn)