The short answer is "as many as it takes to find a home for you".
The long answer is complicated and will likely change depending on your circumstances.
Purchasing a home will most likely be the single largest investment someone ever makes. As such, it is important to make sure you find a home that meets your current, and future, needs.
We tell our buyers to list home qualities and features into three categories:
1) Must Haves -- things you simply can not live without
2) Nice to Haves -- things that would be nice, but you could do without
3) Can't Haves -- things you simply can not live with.
Armed with a detailed list of these three items, a good agent can include and exclude many homes from your potential search. As more homes are visited, it becomes easier (most of the time) to refine the potential homes that may work for you. Be prepared, sometimes you may find things actually move around in your three categories!
Before you begin viewing homes it is important to discuss in detail with your agent the strategy and approach you will take to find, and view homes. Everyone is different.