I'm having this concurring experience, where (while reading Japanese literature) I encounter a Kanji that I know for certain I haven't studied yet, in a word I'm not familiar with, but I can pronounce it correctly anyway (without understanding what it means). As the part of the Kanji is in itself a Kanji known to me, very often (in the cases I've encountered) the pronounciation is the same, and I use it instinctively to get the correct result. I haven't studied any Kanji theory, so perhaps it is a known feature in general Kanji study, but I wasn't aware of it before.
 
Another thing is that with regards to English, I have been fluent with it since I was a small kid, all thanks to "Language Ear". I have no idea what the proper name for the phenomena is. I noticed that I have developed some resemblance of it for Japanese along with hard study. Language skill doesn't seem to be genetic at all.
An article in "New Scientist" magazine said that mastering any skill to genius level is 1% genetic and environment, 29% support and encouragement from others, and 70% sweat. I tend to agree.
 
Third and last, with regards to reading Japanese literature, I've noticed that translated novels by western writers are the most easy to read. Second, native non-fiction articles (tech, biology, history and such). Third, poems. Then novels by Japanese authors (I like animal stories). And the most difficult ones are children's stories by Japanese authors, such as Miyazawa Kenji (took me ages to go through 月夜の電信柱). Distinct regional dialects in stories have no effect on understanding, it seems.
 
Just these few thoughts...

Hi!
 
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This is a common feature of Chinese, so you should find that, once you reach a certain level, you can guess the on-yomi of many characters without knowing the meaning. A lot of times a kanji is a radical plus a morpheme, so if you know the pronunciation of the morpheme you can guess the pronunciation of the combination. Of course, Chinese is nice in that, with very few exceptions, there is only one pronunciation for each character, so your chance of success is fairly high (though there is still plenty of room for surprises). I'm not sure if it works at all with kun-yomi.
 
Do you think novels by western writers are easiest because the viewpoint, voice, and conceptual framework are more familiar, or just because the translators aren't able (or intentionally try not to) make the language of a foreign author "sound" Japanese? Sometimes I think Japanese readers like to have a foreign text sound foreign... as if it were being spoken with an accent.
 
In fact that's probably just as true of Japanese literature translated into English. Unless the original author does it by explicitly referring to places and events, it's often part of the translator's job to somehow convey where the action is taking place. Recently I was reading a collection of stories from postwar Japan that was written natively in English, yet the author still went out of her way (I think a bit too much) to ensure that the readers knew they were in Japan rather than Seattle.

Quote from Hokousha on Oct 10^th, 2006, 5:41pm:

You know, I really had to think about that!  
 
I think the viewpoint and voice are the reason. I noticed that I had difficulties in folklore stories (i.e Japanese writing about Japanese-Only things), but not with scientific and historical articles. The one about the Rosetta Stone was especially interesting (they sure didn't teach that at my school).
 
I just found a Kanji practice sentence that kind of illustrates my point.  
並木の　間を　通る, which means (with an emphasis to my point (Oi! My English isn't that bad!)) "The space of row of trees that I pass through", whereas it would be instinctive for me to express this as "The space of row of trees where I pass through", or 並木の　間で　通る.
It wouldn't come to my mind to consider the space between the trees as an object. It's more like a lack of an object between two trees for me. Learning Japanese sure is a great way to learn about Japanese people.
 
Quote from Hokousha on Oct 10^th, 2006, 5:41pm:

I really like writers who fool around with language like that!  
I used to write drabbles (stories with exactly 100 words). It was difficult to make them sound fluent.
 
Quote from Ainu on Oct 13^th, 2006, 2:50am:

It's ok. Now that I know I wasn't hallucinating, I can google.
 
[Added later]
Ah yes, I would like to append to my list of difficult or near impossible Japanese text, several diary entries from my 20-year old Mixi friend from Tokyo. I'm afraid the linguistic (or cultural?) barrier there goes well beyond any text book or dictionary.
 
  <- Can you guess which one am I?