Belgian ban on full veils comes into force

[Penguin]

Originally Posted by Platapus

Would I be allowed to walk the streets of Washington, London, Paris, or Berlin (or name your capital of choice) wearing a mask that obscured my identity?

it depends. For example in many European countries it is forbidden to cover your face while participating in a demonstration. In some countries, like Germany, even wearing clothes like leather jackets can be seen as "passive armament" if your wear it at those occasions.
Cultural events, like carnival or Halloween are exempt.

Originally Posted by Platapus

After all businesses can still restrict doing business with people who conceal their identity (banks do it) and private citizens can always restrict access to private property to anyone who conceals their identity.

Same here, contrary to libertarian beliefs, we also have freedom of business here. You may deny to do business with people you don't want to deal with - however other laws, like anti-discramination laws also come to play.

Originally Posted by Platapus

So this really comes down to public property and government facilities.

Are there any laws that would prevent me from walking down the street, minding my own business, wearing a mask that conceals my identity?

I am not aware of any in the United States but I don't know about other countries.

What about Public Indecency laws? Don't they also restrict the freedom to wear what you like? Apparently they are not unconstitutional in the US.