In most cases a credit card will be accepted. Of course Germany is still a country which has more trust in real money than this little plastic cards. Sometimes (eg in supermarkets etc) they aren't accepted if you have to pay under 10€ or similar (but seriously, 3,89€ paying with a credit card? Takes way too long and is a bit silly in my opinion).

But I've never experienced that you cannot pay with a credit card at gas stations, coming back to your question.

There should be no problem paying with a credit card at gas stations, but some gas stations may refuse to accept it (I haven't experienced it yet). The American fast food restaurents (McDoof etc.) also don't accept credit cards.

Especially on the Autobahn you should have some cash with you because (sadly) in service areas you have to pay for the toilet (so to even access it). Not on pull-ins where aren't any kind of restaurants but on these with restaurants are often the toilets of "sanifair" and they demand 0,70€ <_<

"There is a strange custom at some of the public restrooms in Germany to leave a half Euro tip for a service attendant who cleans up the public restroom."

This caught me off-guard when I was in Europe. When nowhere lets you use their toilet because you have no change you'll very quickly learn to always keep some handy.

Most 'brand' Tankstellen accept cards. However, some unbranded discount Tankstellen do not. It's better to have cash at hand just for safety. For restaurants etc. here and then you will find a few that do not take credit cards.