I'm wondering if the community knows of any websites which contain the scripts of Japanese TV shows (in Japanese of course)? I'm interested in having something to refer to while watching said anime/dramas/drama CDs. Thanks in advance.

google this forum for links to subtitles to films, anime, etc or maybe someone will give you the links again on this thread.

I wanted to mention this site. It contains transcripts of japanese tv (mostly talk, variety shows) that were ripped from close captioning that aired with the show.
http://o.x0.com/m/27049
I think this site started in 2014. (before this site existed I bothered japanese people endlessly on chiebukuro and lang-8 because i really wanted to know certain dialogue that i couldn't catch off the show)

ALSO sometimes you can find blogs where people transcribe lines from a show. i've found them in the past just from casual internet browsing as well as intentional searches with "" by searching phrases that i heard on the show.

http://www.dramanote.com is the one I know for dramas.
I second the searching with "" tip!! So good, I've done this loads!

dramanote for dramas was already mentioned, but for anime, http://kitsunekko.net/subtitles/japanese/