I totally agree with everything you had to say about Elfen Lied, I watched it all and it's terrible.
Planetes, Hellsing Ultimate, Darker Than Black, Black Lagoon, and Berserk
I crossed out the ones I haven't seen.
Uh, I don't remember humor being that frequent in Berserk.. The humor fit in Planetes because it's about civilians, and Black Lagoon was never serious enough for it to bug me.
There is no fanservice in Planetes. There's only the one scene late in Berserk where Casca is naked (unless you also count that steaming hot water fight between Gutts and Griffith). I don't recall exactly what it was like in Black Lagoon but I have a vague impression it was pretty frequent. I probably enjoyed the action too much to care. There was also the weird thing with those kids but that wasn't fanservice, that just had to do with sex..
I haven't seen the Berserk anime, only the movies and roughly all of the manga (barring the newest chapters) and there are certain comedic elements that disrupt the atmosphere (Puck... all of the elves, looking at you.) I understand that it's in some respects the "Japanese way" to try and lighten up heavy moments and atmosphere with silliness to not overbear the audience, but I would respect a full commitment to theme much more. If your work is depressing, let it be depressing; That's what the viewer expects and accepts and likely part of the reason they are there.
TBH I didn't really take it the same way. Some scenes didn't portray the elves that way at all (consider that, apart from the two in the party, the rest basically
made sport of brutally killing things, including each other, and even rare moments where Puck or Evarella aren't being as serious as the situation demands don't really feel like they're lightening the mood -- and more often than not they're there more as voices of reason/living plot devices than anything else (which is honestly the argument I'd make against them). There's a multitude of reasons for an individual to not treat a serious situation seriously, and most of them are valid in-universe. Unless you're arguing that the simple fact that they
exist is comedic. :/
On the fanservice note, GUNIN, neither of the scenes before or during the Eclipse when Casca is naked are fanservice unless you're really fucked in the head. For one, people can be unclothed without the intent to titillate, and for the other what the absolute fuck is wrong with you if you get off on that. The scene with Guts and Griffith at the fountain, on the other hand...