If it's crap ... We'll tell you
Perfect Blue was kinda ripped off/inspired Requiem for a Dream and Black Swan
Paprika was Inception before Inception (and better in my opinion)
Tokyo Godfathers is a remake of the western, The Three Godfathers (but transformed into a film noir).
Hope these recommendations help and another movie you might want to check out,even though its got robots in it, is Ghost in the Shell. That film is sci-fi but still a film noir (think Blade Runner).
Seems like movies are covered, but if you're looking for TV shows then here's what comes to mind for me.
I dunno about disturbing and gory, but Cowboy Bebop has noir roots and it's sci-fi, but no giant robots. I'm guessing you've seen this show already. Otherwise, shame on you.
Then there's the anime Noir. I've never seen it, but if noir is in the title it must relate to it somehow.
If you're into vampires then Nightwalker: The Midnight Detective is something worth seeing.
Then there's Texhnolyze. That would be the disturbing/gory kind of "noir."
And with the help of the internet I came across an anime titled Kaze No Youjinbou which is apparently a crime drama with noir inspired elements.
Hope any of that helped.