SQL Server Express is a free edition of SQL Server ideal for developing and powering desktop, web, and small server applications. SQL Server 2012 Express has no limits on incoming connections or workload other than the CPU and memory limitations—and it comes in both 32-bit and 64-bit versions.
SQL Server Express includes 10GB of storage per database, easy backup and restore functionality, and compatibility with all editions of SQL Server and Windows Azure SQL Database.
The current four free versions are:
Learn more: SQL Server 2012 Express Editions