The USA is currently proposing the #SAVEAct , which places further restrictions on what kind of identification you need for being able to vote.
For the sake of comparison, in Germany it's technically not necessary to show an ID when voting - you need to show your "Wahlbenachrichtigung", your notification about the election which you have received by mail. You need to register your legal residence in Germany anyway, so you should receive this notification automatically for all elections in which you are eligible.
However, if the organizers have any doubts about your identity, they can ask for some photo ID. This is typically done via the "Personalausweis" - a personal ID card which is mandatory to own in Germany. For people aged 24 or older, this costs €46 to renew, and it is valid for 10 years. It is also valid for travel within all #EuropeanUnion member countries, so you don't need a travel passport for those.
A travel passport is also valid for this purpose. It costs €70, and is also valid for 10 years.
