MSDE was the "local-only" version of SQL Server 2000 - there is no more recent version of MSDE.
As of SQL Server 2005, the free version (which you can legally use FOR FREE - even for commercial applications) are called SQL Server Express. The current version is SQL Server 2012 Express (with the 2014 version coming out soon) - I would strongly recommend to use that version (and not use another already 5-year old system like SQL Server 2008).
Those are still a server-product that should be installed on a central server - but you can also use it locally on a PC. The main limitation is that the Express versions only support 1 CPU, up to 1 GB of RAM, and have a database size limit (up to 4 GB for 2005/2008, up to 10 GB for 2008 R2/2012).
See this Microsoft site for more information on SQL Server Express
If you have an issue with those limitations - then yes, you must purchase official licenses for SQL Server - either from Microsoft or from an authorized reseller. The different options and prices are just way too broad to list here - you'll have to ask Microsoft or a reseller for a quote