It varies by the age of your house. You might find clay, cast-iron, or plastic sewer pipe. Clay and cast-iron are older types; plastic is the newest.
Just because a house is old doesn't mean it won't have plastic sewer pipe. As the years wear on, sewer systems deteriorate, necessitating replacement.
You might even find cast-iron or clay sewer lines at a new house, though this is not likely.
Sometimes--as is the case with the line shown here--you will find all three types of sewer pipe tied together.
In terms of home renovation, you may find yourself being steered in the direction of PVC or ABS plastic pipe over clay and cast-iron. While plastic pipe is undoubtedly easier to work with, clay and iron have strong points: long lifespan and strength (for the iron).