I'm surprised that there haven't been more recommendations for Japanese authors, so I thought I'd introduce some of the works and authors that really got me interested in Japanese literature, as well as some that I've discovered more recently, but also enjoy.
When I first read
Kokoro, by
Natsume Soseki, I was amazed that I could feel such a strong connection to a novel that had been written over a hundred years ago by an author coming from a completely different culture than my own. Soseki writes with a very profound insight into the human mind and emotions, and the themes he addresses in this novel are so universal to the human existence that I would find it difficult to imagine that anyone could read it and not be powerfully moved.
For something a little more contemporary, I've also always enjoyed the works of
Haruki Murakami, who has a very unique world view. Both his novels -- like his epic
The Wind-Up Bird Chronicle, or
Norwegian Wood, a tragic love story that is more 'realistic' than his typical works -- and his short stories (of which
this is an excellent collection -- "On Meeting My 100% Perfect Girl One Fine April Morning" might be my favorite short story ever) I would highly recommend highly.
For anyone interested in science-fiction or dark humor, I'd also recommend Yasutaka Tsutsui, but I don't think that his works have been widely translated. I especially love his short stories --
Ore ni kansuru uwasa ("A Rumor About Me") is a wonderful collection.
If you like mysteries, you may want to check out Miyuki Miyabe, whose works (like
this one) are just beginning to make their way into English translations. I've never read the translations, though, so I can't speak as to their quality. (Though I believe the translator is Alfred Birnbaum, who did a pretty good job with some translations of Murakami short stories that I read a while back, so I imagine these would be of similarly high quality.)