Naturally there are many, many contemporary Japanese artists worthy of attention. Here are some links to a few of them.
To start with, there was a famous exhibition at the Asia Society in NYC called
"Little Boy" in 2005; a 2007 exhibition at the same place called
"Making a Home" was also very interesting.
Probably the most famous contemporary Japanese artist is Takashi Murakami. There's a
Wikipedia entry with some useful links. His
page at Kaikai Kiki, the art company he founded is also useful, as is
this page from an exhibition at the Museum of Contemporary Art (MOCA) in Los Angeles. (There are tons of YouTube videos featuring Murakami as well.
Here's one where he's interviewed by fashion designer Mark Jacobs about, among other things, Murakami's
collaboration with Louis Vuitton.) And he shows in
galleries and other
museums too.
Besides Murakami,
Kaikai Kiki handles a number of artists
Yamamoto Gendai is a Japanese gallery handling many contemporary artists.
Other artists to look at: