We don't have a general speed limit on the german Autobahn BUT we have localized speed limits which sometimes last for 10,20 or even 50 km. And to avoid problems with the german law (no general speed limit on the Autobahn), some local authoroties are pretty clever: they put up a speed limit let's say for 20 km and then there comes a short part of 5 or 10 km where there is no speed limit anymore. And guess what happens after this short part.
Some speed limits are also in effect only at certain times, for example the speed limit from Ulm to Munich on the A8.
From 6 am to 8 pm only 120 kph are allowed. Between 8 pm and 6 am, there is no speed limit.

You have to be careful, it is highly recommended to avoid exceeding the legal speed by more than 20-30 kph on the Autobahn if a speed limit is in effect. You still have to pay if they catch you but you avoid risking more serious trouble. Playing the dumb tourist, playing it nice and telling the police that you're sorry, also helps most of the time. Starting verbal fights, looking angry, etc. only raises the tension and nothing good can come out of it. Just a hint. If police stops you on the Autobahn in an ordinary car (usually they pass you and a POLIZEI display lights up or they flash you with a red light from behind) and not a police car and if they're dressed normally (you can still see the guns and most of the time they also show their badges) and not in uniform, you're in trouble and there is no need to argue with them or playing it tough. They have you on video, including license plate, speed, etc. Tell them you're sorry and play the dumb tourist and you might get away with a ticket only. If you were really fast (let's say 280 in a 120 kph zone), don't say anything and I suggest getting a lawyer.

Better keep your eyes open, always look what is behind you and pay attention at the distance of the car behind you. They usually drive limousines or station wagons and try to keep a steady distance for some time to be able to put your driving on video, including a correct and steady speed.

But I shouldn't drive you to boredom with too many details.

The Autobahn from Stuttgart to Munich is very nice but as I said before, it is more interesting at night because this is when there is a good chance that there is no speed limit on most of the length. We also have electronic displays which indicate a changing speed limit and sometimes, radar traps with phot radar are not far away. If a large display over the street indicates 120 kph speed limit, this is official, you have to follow it. The speed limit is only over when an additional electronic display or ordinary traffic sign indicates it.

In Austria, you have to be careful with the speed limit. Austrian police can "guess" your speed and they are traffic gods. Meaning: if a police officer stops you and say you went 160 kph instead of the legal speed, his word is the law. Don't start argueing, these guys are well known for being pretty nasty to tourists. Same with french and swiss police, careful!
Be careful around Berlin, there are lots of speed limits in effect and tons of radar traps and police patrols. Also be careful on your way from Berlin to Munich (you should definetely visit Leipzig and the Porsche factory there!), there are some speed limits and lots of radar traps incl. video patrol cars.

Around Munich, there are a lot of nice little country roads, for example around lake Starnberg.

If you need more details, send me a PM or eMail.