I'm sure I referred to them as "fag-rock" at some point - and I still do because that's what they are - but I like Pornography and - even more - Head on the Door. This is all well after the fact - I think it was the late 1990s when I first played a Cure album. I never got into Disintegration at all, though.
For Depeche Mode there's only a couple of albums that I like, but they also have singles that I like, though mostly for '80s nostalgia.
I actually *saw* Depeche Mode in concert a few years ago, though that was at the urging of my wife. Not as payback for making her see Steve Hackett - that particular payback came in the form of Barbara Streisand.