I am currently looking at a house in New England that dates back to the 1820's that has a sagging floor in the living room. The floor dips down about one inch near one of the walls and I was told by the owner that it has been and is structurally sound and that sagging floors are "normal" in older homes. Is this in fact true and if so what would the typical amount of sagging be?
Assuming the sag is new/progressing.
There are countless hundred+ year old homes with proper structure that have floors that don't sag, bounce or shake.
Sagging is never good. Sagging is a sign of either poor engineering to begin with or structural damage done later.
bcworkz does raise a good point about older foundation methods and short term sags that stabilize. I still maintain that even in such cases, a sag isn't "good", but it may not be deal breaking.
Just to play devil's advocate, there are also many old homes that have suffered minor subsidence and now are completely stable. Modern homes with reinforced foundations should never suffer from differential settlement. Old homes using outdated foundation techniques could suffer from some differential settlement in their first few dozen years, then stabilize and stay that way the remainder of their lives. This sort of settlement, though not ideal, is not cause for alarm.
Other such homes are founded on unstable soils and continue to shift and settle for their entire lives. This cannot be good. As a casual visitor, it's difficult to tell what is not alarming and what is bad. It would take extremely accurate measuring equipment and a good long time period to determine whether the structure is still moving or not.
This house is actually pushing 200 years, if it's just an inch low in one spot, I'd say it's probably in good shape actually. It's still not normal, but it's not unusual either.