The United States from the foundation to 1875, when the first immigration control legislation (the Page Act) was passed. Though, despite the Page Act, immigration remained fairly free for several decades thereafter. Immigration control was primarily an initiative of the Republican Party, which at the time was the party in favor of a strong central government, tarrifs, industrial subsidies, central banking, fiat currency, and imperialism: they wanted to keep out Germans and other ethnic groups that tended to vote Democrat (Jefferson's Democrats: aka libertarians).
Great Britain from the beginning of modern history until 1962, when the Commonwealth immigrants Act was passed. Though I do seem to vaguely recall some law(s) passed after WWI, don't remember the details - but the point stands, Britain had no immigration control for most of its history.
Most nations throughout history have had totally free immigration (except in wartime). Controlled immigration is a modern concept, and a bad one.
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