English is obviously the major one, but I've heard German was spoken by a significant number of people in Pennsylvania, for example. If there isn't a lot of variation, I'd be interested to hear about regional dialects of English that we know about from that time, or important Native American languages, if their distribution is interesting. Really I'd be happy to hear information about any time from 1760-1800.
Ignoring regional dialects of English:
English, of course, was spoken by a large portion of the white population of the 13 Colonies
French was spoken in Quebec, as well as in small scattered encalves throughout the Ohio Valley and down the Mississippi all the way to Louisiana.
Spanish was spoken in what is today Florida and the Gulf Coast
Dutch-speakers lived in the Hudson Valley was well as in what is today Northern New Jersey. Dutch did not go extinct in these areas until the mid-19th century.
Various High German dialects were spoken by a couple of different ethnic and religious groups who migrated to the New World from Germany. The Amish of Pennsylvania are probably the best known.
Then, there were the Native Americans who spoke hundreds of different languges. East of the Mississippi, there were three major language families represented: The Iriqouin langugaes, the Algonquin languages, and the Souixan languges (Catabawan?). These are broad languges families. An Eastern Alonquin language like Passamaquoddy is as different from a Central Algonqin Language like Ojibwe, as French is different from Swedish, maybe moreso.