I don't know any streaming websites that include Japanese subtitles, but you can download Japanese subtitles for animes from http://kitsunekko.net/dirlist.php?dir=s … apanese%2F or for dramas from http://jpsubbers.x10.mx/Japanese-Subtitles/ or http://www.d-addicts.com/forum/subtitles.php#Japanese.

The subtitles posted at d-addicts are often timed to match some torrent releases, but the subtitles at jpsubbers are not.

http://forum.kitsunekko.net/viewtopic.php?f=2&t=2 mentions some of the sources for the subtitles at kitsunekko.net.