Internet
Internet cafes are available in the main towns.
Internet cafes are common, but usually small, local businesses. You probably won't have a problem finding at least one in even smaller towns or large villages.
Phone shops will often offer internet access, too.
Most hotels offer internet access. Inquire your hotel about access possibilities and rates before booking.
From every phone - regardless whether private phone, hotel phone or mobile phone - you can get free dialup internet access immediately without sign-up.
Just the normal land-line phone rate applies when you use one of the numbers listed at The Foxy Phone Page. These numbers can be used even for internet access from abroad.
In several cities, projects exist to provide free "community" hotspots for wireless networking.
Passenger lounges at some airports and central railway stations also provide internet access to their customers.
Public libraries often offer Internet access, however usually not free of charge. The libraries are open to the public for free, taking a book home might require you to get a customer card at a low fee, though. Note the National Library in Leipzig, Frankfurt am Main, and Berlin is not free.
Wi-Fi Internet access is not yet very common in Germany.
However,in several cities, projects exist to provide free "community" hotspots for wireless networking. It is usually available in most airports, hotels and some cafes in larger cities.