Well, several EU countries have de facto requirements for you to carry ID at all times. The US allows one to go without identification for pretty much all purposes. Heck, most countries allow much more leeway for stop and search than the US does (being shackled by the fourth amendment here).

In France, while the law now states that one can prove their identity by any means, it is up to the officer asking you whether they accept your proof. So, if the officer doesn't accept 100 non-government documents and you don't have your ID with you, you're in trouble. Not carrying ID at all times can lead to arrest.

In Germany, every person must posses a national ID card, but there is some leeway about presenting it to a requesting official (it doesn't have to happen on the spot). Nevertheless, most carry one all the time.

In Greece, ID cards are compulsory and you can be detained for not presenting one upon request.

In Italy, you're only required to carry your ID card when outside your local authority, but unless you know all the police in your local authority, you're simply required to carry it always. Failure to present ID can result in detention until you can be identified.

Portugal requires you to present your ID card upon request, but doesn't mandate that you carry it at all times.

China requires every citizen to carry an ID card which will soon have biometric data about the person including reproductive history.

In Spain, you are required to present ID, but failure to do so won't end in arrest unless there's another reason to arrest you and you can request that the officer come to where you store the ID.