MSDE (Microsoft Data Engine) is the answer. It comes with your VS.NET product, with free redistribution rights and it's the full SQL Server 2000 engine with some limitations (concurrent connections and maximum DB size as far as I can remember). See the product spec to learn what are the specific limits and if they fit your needs. The great thing of MSDE is that your client effortlesly upgrade to the full SQL Server 2000 package if needed.
This was first published in August 2003