The Turks are an Altaic people (going by language), and so are related to a whole host of other peoples -- Turkmens, Kazakhs, Uyghurs, Azaris, Tatars, Kyrgyz, Uzbeks, Mongols, Tyvans, Yakuts, Evenks, and Manchurians, to name a few. The Altaic language group is incredibly widespread, and also fairly homogeneous, as language families go; a Yakut and a Turk can make themselves understood to each other with not much effort. It's quite possible Japanese and Korean should also be classified under the Altaic language family, and Finno-Ugric (including such languages as Finnish, Estonian, Hungarian, and Saami) may also be related to the Altaic languages.
The Altaic peoples likely originated in the Altai mountains (hence the name), and their main cultural distinction historically is that they have been nomadic herders in the plains and mountains of central Asia, as contrasted with the Indo-European peoples, whose originated as herdsmen like the Altaics but borrowed farming at an early date from the Semitic peoples and have been agriculturalists ever since.