Blanket refusal to get an ID card or passport will get you into trouble in some countries as a citizen (e.g., Germany). Possible fines etc. aside, establishing your ID in a lot of situations will get quite difficult.
Germany requires you to have an ID document from the age of 16. You do not need to carry it however (there are a few exceptions, e.g. if you work in construction or the like where tax evasion/cash in hand is not uncommon).
Inside the EU's Schengen area, the ID is only needed at borders.
Again, once inside another Schengen country, you do not need to carry it around.
I'm not sure if the same rules apply for foreigners though, once they are inside the EU.
From trial and error over the last five years I'd say three out of five airlines will let you board flights using your driver's license as ID. They always complain but they let you through anyway.
ID checks at Schengen to Schengen borders are absent anyway since many years so this isn't a big surprise.
That said: I'm a white man.
These rules apply to everyone by law.
Sadly, the less 'Caucasian' your phenotype is, the more likely your experience with EU security forces will be for them to expect you to carry ID -- despite the above rules.
And boarding a flight with your driver's license if you are not white -- forget it.
Racism is everywhere though. It is just especially painful to see in this context.
The greater point, I think, is that everywhere else in American where I deal with the government I am required to present some form of ID. They even give you a list of a dozen or more valid IDs you can use.
However, arguably the most important interface with the government, voting is a place where I don't even have to validate I am who I say I am.
They don't really care who you are, they only care if you are allowed to vote. At least in theory, of course weird stuff probably goes on every year due to the size of the US.
