SQL Server Compact Edition is advertised as a small embedded database that can easily be included with a Windows Forms application during deployment. According to some of the informal documentation online, one of the ways in which this is suppossed to be possible is to include the SQLce DLLs in the application file of your deployment. However, the official documentation (SQl Server CE Books Online) only mentions the options of installing the product via .msi on the client machine, or using a Click-Once application.
I would much rather deploy without having to do Click-Once or a full-install of SQLce. So I tried copying in the DLLs from the C:\Program Files\Microsoft SQL Server Compact Edition\v3.1\ on my computer into the application directory during deployment, and it worked (!). There are 8 DLLs included, and through trial-and-error I was able to determine that (at least in my case) only four DLLs were really needed when deploying: