What are the most popular German TV shows? Are they viewable online?

I don't know where you'll find them in the US, but two shows that I watch, for no better reason that they're easy enough for a non-native speaker to understand are "Die Rosenheim Cops" (very catchy theme music) and "Küstenwache". If you're looking for original German-language scripted drama, these are usually shown on Das Erste, ZDF and the various ADR regional affiliates. RTL, ProSieben, Sat1, etc. usually broadcast US shows dubbed into German and the usual international reality junk formats. EDIT: No sooner do I write the above, then I catch "Sherlock" dubbed into German on Das Erste.

I sought to do the same thing, and ended up subscribing to Verizon Fios' German language programming. I watch many different programs, and am finding it VERY helpful to hear the language on a daily basis, especially the Deutsche Welle news broadcasts, Euromaxx, and Im Focus. Great for hearing new modern words / techie words that I've never known, plus refreshing my memory of words that I should know, but have forgotten. Strangely, some of the "reality" programming that mimics our talk shows, courtroom shows, etc. is also helpful ... Zwei bei Kallwass, Richter Alexander Hold, Britt, Harold Schmidt, etc. I know some of the Deutsche Welle programming can be viewed online, at least. I'm not sure of the others. Youtube is also another option - sometimes I just click around on it til I find something interesting "auf Deutsch." Hope this helps at all.

For Austrian German, you can watch Wien Heute. It is a daily news show for Vienna. They also have news for other regions in Austria as well. The ORF site also has many other shows you can watch over the internet. http://tvthek.orf.at/programs/70018-Wien-heute

Watch some "Linden Strasse", one of the longest running shows on German TV. See if you can find "Perfect Dinner", where 5 people cook for each other, and then they vote who did the best job as a host or hostess. Everything gets judged, from the food, the wine, the table decor, and even if the cook was stressed. "Quiz Taxi" is fun, plus you learn interesting facts too. Or perhaps a little "Wetten Das". More drama? Add in some "Tatort" which tends to film a lot in Frankfurt, or one of the law shows showing court cases. I learned my German by watching game shows done by Juergen von der Lippe, and kids shows, like "Sendung mit der Maus" as well as the German "Sesam Strasse." One thing that I did notice when learning German, was that if I watched a show that had been dubbed into German, I understood it better, simply because the phrases made sense to me. Watching pure German shows was a bit more difficult. A plus with the DVD's over here is that you can watch them in multiple languages, with the subtitle either in that language or in German, so if you watch it several times, you start to get more of an idea for the vocabulary, sentence structure, as well as pronunciation. If you can do this with the DVD's in N. America, this will help you.

"arte" is a relatively high brow Franco-German public broadcaster. It isn't terribly "popular" (I think its market share is 0.5% in Germany), but it puts the last seven days on the net: http://videos.arte.tv The show I would recommend is "Karambolage" where they explain French and German everyday culture to Germans and French respectively. A treat for people who are interested in these cultures. You can find the crime show "Tatort" that Jo mentioned on the ARD site: http://mediathek.daserste.de/sendungen_a-z/602916_tatort A review of one Tatort episode on Andrew's blog: http://andrewhammel.typepad.com/german_joys/2012/05/a-very-special-socialpedagogical-tatort-episode.html Unlike "Je" I actually feel that the public broadcasters (ARD, ZDF, 3sat, arte, Phoenix, and so on) are the only ones worth watching.
But of course taste differ.

Crime shows are very popular in Germany. Check out "Tatort" on ARD. It's the longest running crime show in Germany/Austria/Switzerland. I grew up with watching them faithfully on Sunday nights. There is a search window "Sendung verpasst?" on www.ard.de where you can type in the show's name and it leads you to the online video. During my latest trip to Germany I discovered another crime show I like very much "Ein starkes Team": http://www.zdf.de/ZDFmediathek#/kanaluebersicht/322/sendung/Ein-starkes-Team ZDF also has a "Sendung verpasst" search window on www.zdf.de. You can try out other crime shows like "Kommisarin Lund", "Kommissar Stolberg" and more!!! Jo,
I LOVE "Perfektes Dinner"! Chefkoch.de has a few discussion threads where participants talk about their experience (they are allowed to do so after the show has been aired). Very very interesting! Unfortunately, I haven't been able to find an online video stream that does allow me to watch it from Canada :-((((((

Jo is right, it does help to get a DVD of a German movie and watch it with German subtitles. That's how I get my teenagers to watch the occasional German movie. And I turn them on when I watch a Bavarian or Austrian move - movies like "Wer frueher stirbt ist laenger tod" (Bavarian) or "Silentium" (Salzburg!) are wonderful but even my group of German friends, mostly "Nordlichter", was not able to watch them without subtitles ;-)

"... saying how high quality German public broadcasters are is like saying the absolute majority of German public broadcast programs put the American commercial and public ones alike to shame ..." That is IMHO a bit of a straw man argument: 1) no one here in this discussion has used "high quality" until now except you. 2) in my view "high quality" means just "high quality" not "put everyone else to shame." "Intellectual Property" (and a good chunk of that is TV and movies) is an extremely important US export category to Europe for a reason. And it's not (or at least not mainly) "cultural imperialism," but the simple fact that Hollywood and the American TV industry reliably churn out a ton of "watchable" to "excellent" stuff each year. My point was that according to my personal taste, 99.9% of the productions of the German commercial broadcasters (RTL, Sat1, Pro7, VoX, and so on) are rubbish, while I can find decent stuff among the productions of the public broadcasters. That doe not mean that they don't produce horrible stuff as well. Because, oh boy, they do.
And that ranking of German public broadcasters vs German private broadcasters implies nothing about the relative merits of US broadcasters.