Remember, I'm an American writing the blog for Americans to grasp the inner workings of German culture.
You could live in Germany for thirty years, and never get pulled over by the cops. You could live in Germany for twelve months, and get pulled over three or four times by the cops. It's a statistical odds thing.
There are basically only two scenarios which you will end up with your car being pulled over and reviewed.
Scenario one: you are speeding down the autobahn and hit a stretch where there is an actual speed limit and you've exceeded it.....with a unmarked German cop car which pulls you over. It'll usually be near a rest-stop and they will tell you follow them to the rest-stop entry.
The event is pretty scripted out. The cops will have a computer video-file of the speed event, with your car in full view and the speed which you were reaching in display. They will ask you come over to their car....show you the video.....mostly to enforce the idea of a lesson learned. Play the game along and simply be agreeable.
They will ask for your license, the registration, and insurance paperwork. If you are lucky.....that's the full extent of the review. If they go to ask you to open the trunk.....it's to check the first aid kit and see what you have in the back of the car. At each point of resistance on your part.....they will simply make it more uncomfortable.
The speeding ticket? You can pay the fine on the speed....usually meaning less hassle and no points. Or you can simply sign to have the ticket sent to you and dispute the whole thing.....meaning potential points taken off your record. This is usually why you should always carry 100-Euro on you....just for fine purposes.
Scenario two: it'll be a two-to-twenty man patrol who set up a stop-point and simply pick cars to check out. It can be near the autobahn or on a street, on in the middle of nowhere.
This check will usually involve a review of your drinking state, your registration, your license, and the contents of your car (usually looking for drugs). They might also review any modifications to the car.....which affect safety or violate German codes. An example here....would be a muffler modification which makes the exhaust sound 'stronger'.....which means a minimum of a ticket/fine.
It's a popular thing in major urban areas...like Frankfurt, and it'll occur to a greater extent on Friday and Saturday evenings. If you don't hang out or drive on such evenings....the odds are against you ever facing up to such an event. If you live way out in the rural regions of the Pfalz.....never traveling much.....it's almost a zero chance you will face this.
Some of these events are organized to such a level....that there is a tent set up with computers and testing equipment there. Sometimes.....even the Zollamt authorities will be around to ask questions over cash in the car or contents.
In all the years I've been in Germany.....I've run into the second scenario only on one occasion...while exiting a US military installation. They wasted two minutes reviewing my paperwork, and asked to see the contents of my trunk (never even asking for the first aid kit). That was it.
My general advice....be friendly and simply accept it as part of the game of living in Germany.