Some folks even know further back than that all the way to the original pioneers and settlers in America. There is even a Mayflower society for those immigrants of clans who came over on the passenger ships from England, Scotland and Ireland, or other European countries during or after medieval times. Today the Mormon church collects genealogical records from all over the world. Those records include information about marriages, deaths, land records, births, christenings, deeds and wills. Some of the church parish records and census records across the years are also transcribed onto microfilm or put into the international genealogical index.
Surnames are a good way to know the probability of relationship.
Obviously, if someone carries your same name, there is greater likelihood of their being a common blood line. But sometimes surnames are spelled much differently even with the same sound. This has occurred for many reasons. Many times they are just different family names and families. Other times though, even the same families have spelled their surnames differently.