Just so you know, the idea from this post comes from the book Ikebukuro West Gate Park because, as normal it is that the first 2 volumes made me think about Durarara!! (I'm still convinced Narita read it), the last one made me think about Tiger&Bunny, which is a little less normal. Unless there really is an evil organization that tattoos its mark on their members called Ouroboros in Japan but I highly doubt it.
Then I started to be convinced that everyone involved in pop culture in Japan somehow has read IWGP (which actually you should do too) and wondered what other influence I could maybe spot.
Sadly, my knowledge in litterature is primarily focused on European authors, but it doesn't mean you can't find any influence from them. Actually, these have been adapted a lot or at least a lot of Japanese anime have been influenced by those books.
Also, not counting light novels.
#1 The actual adaptations
Actually, there are a lot of those, even more in manga than in anime (Hell, they even made a manga version of Marx's The Capital).
I actually haven't seen a lot of those for which I have seen both the anime and read the original version. The only anime I can think of right now is Genji Monogatari which was a pretty good though really shortenned, adaptation of the book.
There's Howl's Moving Castle too and a lot of Ghibli works. Howl is a pretty good adaptation with Ghibli's defining style added to it.
Some others : Aoi Bungaku (pretty good initiation to Japanese "classical" litterature), The Count of Monte Christo, The Three Musketeers, etc etc
Please by all means add to this list.
#2 The influences
Again, those are everywhere because authors are always somehow influenced by something they have read or seen or whatever.
The one that comes immediately to my mind at this is actually a manga called Tsumi to Batsu that's been loosely based on Fyodor Dostoyevski's Crimes and Punishment, but set in modern times.
Some of those include works like Le Portrait de Petit Cossette (excuse me while I cringe at the French), Kuroshitsuji (no matter how you look at it, it's Faust), RomeoxJuliet (which is self explanatory, though I have actually never seen it so I assume it's only loosely based on Shakespeare's original), the Fate series (because some of the heroes are from books), Code Geass (because to me it looks like the whole thing is, loosely, based on the Bible) and probably a lot of others.
#3 And everything else ...
Actually this shouldn't really exist, I just can't really consider names a legit influence on a story.
But if you think about it, character names are often based on already existing characters.
Like, in Katekyo Hitman Reborn you have a whole team of characters whose names are based on demons, in Ao no Exorcist you have Mephisto which is from Faust.
There must be some more but I forgot.
In the end I guess that post wanted to summarize once again how amazed I am at how fluid Japanese are with categories. I am not saying French don't do it, we too have our "anime" loosely based on the Three Musketeers, but it's such a rare occurence that I can't help but admire how Japanese do it.