(Because, in Germany, even if you're an ADAC member, you'd be hard pressed to find an ADAC-affiliated office to pick up a map from...)
The bottom line is that if you're having a problem and you're in an automobile (doesn't have to be yours) AAA will do their best to help you solve that problem.
Unlimited, free, high-quality paper maps are just another perk. Walking in to a member branch and walking out with maps is just the beginning: a AAA employee will help you plan out a road trip, and make what's called a TripTik, which is a custom spiral-bound route map, with various sorts of amenities you can choose pointed out for you.
There are campgrounds as well. It's truly remarkable how much AAA offers.
However, I would caution you that some of the benefits that used to come from being an AAA member have been severely curtailed. The towing benefit, in particular, now has quite a few restrictions on it.
Not to mention the roadside assistance and towing coverage. I take long roadtrips too. The couple times that AAA has saved me make all the yearly dues worthwhile. E.g., once they arranged a 300-mile tow from a small coastal town back home; it took less than an hour to setup and didn’t cost me a dime. The alternative would have been paying next-day air freight on a Mercedes alternator and battery, and staying another 2 days to get the work done.