There is not one answer, but here are some things to keep in mind.
When you get started, take a day and look at different type of homes. Look at some that are old and some that are newer — construction styles, layout preferences and materials change quickly and deciding on the era of construction you prefer is important.
It is also important to decide on how much land you want and in what environment. Urban neighborhoods tend to have the smallest lots, but are closer to amenities. The suburbs give you a little bit of land and newer schools, but tend to be more car dependent. Rural areas give you the most space, but are furthest from the shopping and work centers.
So how many homes you need to see before buying can vary based on what type of housing you want and how long it takes you to decide.