Recently, there was this thread:

http://www.italki.com/discussion/82720

Of the things I threw at the thread-opener in my lengthy German-languaged answer, <em>Faszination Wissen</em> and <em>Quer</em> (both on bayerisches Fernsehen) are the only ones with subtitles I'm afraid. They do not have particularly easy language, it's normal content for adult native speakers.

If you want to browse a bit on your own, look at "Sendungen A-Z" on the Mediatheken for an alphabetical list of programmes. Some have subtitles, some don't.

Maybe you want to just flick through the DVDs you own? Maybe you already have some copies at home that include audiotrack + subtitles in German. German-languaged dubbing of films and series is typically done on a high level of voice acting, recording quality and everything. Knowing the story already might be worth something.

Oh and there is also content to be found on Youtube that has proper "handmade" subtitles (rather than the rubbish automatic ones).

You should check on ARD Mediathek, there's a lot of material there, some have subtitles. You can also look on ZDF site, I watched a lot of movies and documentaries with subtitles. Yet, these subtitles are not complete, they are rather some kind of abridgements what is actually spoken.

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