www.onlinetvrecorder.com

Chip (computer magazine, see www.chip.de) wrote in 2012 or 2013 that this is legal. 

There is more than enough on ZDF sendung verpass, mediathek. I would advice that, not the ARD, since there are more entries with subtitles (in German) on ZDF. I think the subtitles help to follow the German, even if they are written in German. Especially if there are series in southern dialects. SOKO Kitzbuhl, SOKO Wien. That stuff. It would keep you occupied for hours! There is one setback, it are mostly police stories. No comedy, no action movie. And it are mostly TV series, no movies. If you are focussed on learning German, however, it is entertaining enough.