German series I'd recommend:
Dr. Psycho
Probably cancelled after only 2 seasons, this show earned critical acclaim. It's a sort of comedy crime drama about a psychologist with a failed marriage who is supposed to support a team at the CID in Cologne. It's out on DVD, but I don't think they come with subtitles. One of the best German series ever but might not translate well.
Ijon Tichy, Raumpilot
A mini-series based on Stanislaw Lem's The Star Diaries of only 6 episodes. Has very low production values but makes up for it with enormous creativity. It's also out on DVD but without subtitles and everyone speaks with a heavy fake Eastern European accent, so it's probably pretty hard to translate.
Irgendwie und Sowieso
Another mini-series that shows life in provincial Bavaria in 1968. A cult classic. Out on DVD, again without subtitles.
I could also mention Pastewka, a comedy series evolving around the (fictional) life of comedian Bastian Pastewka that allows us a view behind the scenes of the media. 3 seasons, so far (season 3 is pretty weak, though), all out on DVD, again without subtitles. A 4th season is planned. It is supposedly based on Curb Your Enthusiasm (I have never seen it), so it might not be very exotic.
Someone else mentioned Tatort. This is a regular crime drama, that's been on since 1970. Each episode is 90 minutes long, there are several pairs of police investigators in different parts of the country. Each episode concentrates only on one of those pairs. It's a good show to see different parts of Germany and it's pretty straight forward. However, it is a bit hit and miss. Some episodes are really bad, others are really good. New episodes air any other Sunday evening, older episodes are repeated at different times. The former GDR equivalent Polizeiruf 110 is pretty similiar. Other good crime dramas would be Soko Leipzig (takes place in Leipzig) and Wilsberg (a former investigator/now bookdealer investigates in Münster).
