What to put in "affiliation" field when submitting paper without affiliation?

As noted by @mankoff in a comment on Does one need to be affiliated with a university to publish papers?, you can use "Independent Scholar":

Here is a recent paper published by someone affiliated as "Independent Scholar": dx.doi.org/10.1175/BAMS-D-12-00171.1

For completeness’ sake, I mention that another option would be to give your private address as an affiliation. Here is an example for this. Here is another one (affiliations are at the end of the paper)¹. This one only lists the city and country part of the address².

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¹ Credits to Jessica B for pointing this one out.
² Credits to Cheersmate for pointing this one out.