We visited a couple of cemetaries in PA - an old Church near our home had graves from the 1700's......it was eerie but I liked knowing that here we were, 200-300 years later thinking about that person........
There is a old church cemetery in Hillsborough, NC where my (6x?) great-grandmother is buried.
She died during the Revolution and has the oldest tombstone in the cemetery. I've been there a couple of times and it's an amazing experience.