The Autobahn has become very tiring to drive on. Most people somehow decided that its easiest to drive in the middle lane at slow(ish) speeds, while the right lane stays empty for long stretches. Since you are not allowed to overtake on the right lane, both the left lane and the middle lane are clogged most of the time, averaging about 100-120 Km/h. If the public transportation was a bit more reliable and cheaper I would sell my car.
I've been fined on German highways for going too fast. Memes like these are myths. It is based on fact that there is no default upper limit on highway. But there are speed-limit signs on German highways.
I think it's based on the (fahrt fahrt fahrt auf den) Autobahn. Now, I'm not german so I could be wrong, but here's what wikipedia says regarding speed limits on the autobahn:
Much of the system has no speed limit for some classes of vehicles.[1] However, limits are posted and enforced in areas that are urbanised, substandard, accident-prone, or under construction. On speed-unrestricted stretches, an advisory speed limit (Richtgeschwindigkeit) of 130 kilometres per hour (81 mph) applies.[2] While driving faster is not illegal in the absence of a speed limit, it can cause an increased liability in the case of a collision (which mandatory auto insurance has to cover); courts have ruled that an "ideal driver" who is exempt from absolute liability for "inevitable" tort under the law would not exceed Richtgeschwindigkeit.
So, it certainly seems there is a basis for the jokes, even if they aren't 100% historically accurate.