Since 1938....Germans have been required to have an identity card. To be honest....the original concept started with the Nazis, who mandated that all German men (of military age) had to carry the state-sponsored ID with them.
In the early 1950s, it went through an update, and all Germans over the age of 16 (men and women) were required to have the ID on them while traveling, voting, or in any public situation where an ID might be necessary.
Current cost today? Well, it's not free. It runs roughly around 28-Euro ($34 American). If you are a student, there's a discount of around twenty-five percent.
In 2001, they went to a more modern card which had security features built into it....mostly because of the number of fakes on the market. Around six years ago (2010), they went to one with a RFID chip on the card....so it stores some basic data about you.
One of the little odd factors that might surprise most Americans is that the German driver's license isn't necessary considered a prime or accepted ID concept anymore. Since everyone is required to have a national ID card, if someone asks you for an ID (cops, banks, Bahn, etc).....they don't have to accept the driver's license, and may insist on the national ID instead.
Voting and the ID? Several weeks before an election....you will have a letter sent to your home and just note the day and location that you can vote. It'll have a sentence within the letter mandating that a state identity card will be mandatory. You ought to show up with the letter and the state-ID, but they will allow you to vote without the letter.....as long as you are on their database listing and have a state-ID. Without the state-ID.....you aren't legit.
As you can imagine, this state-ID is kinda important at age 16, because German law allows a kid (of sixteen or above) to buy and consume wine and beer (not hard alcohol). So, this is one of the top priorities of a kid who has his or her birthday coming up, and making a trip to the county office to get their state-ID.
How many Germans exist without the state-ID? There's just not much you can do, in terms of bank business, or county/city business, or the affairs of existence in Germany without the state-ID. Maybe there's some guys living out in the city parks, or under bridges without it....but the vast sum of German citizens (99-percent) have such an ID.