I agree that people of old moved around more than we might think.

In addition to those deeflint01 mentioned, I'd add the Turkic peoples of Central Asia. They've been invading, trading and settling in Europe (and throughout Asia) for centuries. Some Turkic peoples are Tatars, Bulgars, Ottoman Turks, Kazakhs and possibly the Huns. The Mongols assimilated into most of the Turkic populations after their empire broke apart.