Believe me, people/organizations that really require a database, do not consider Access. Too slow and bloated. Microsoft also offers (an Express version of) MS-SQL Server. the free version has a limit between 4 to 8 Gbyte if memory serves me right. Oracle also offers a free versions of their Database software (based either on their 10g or 11g version). Their limit is 4Gbyte.
Both databases are the real deal and waaaaaaay more interesting to play with then Access. Excel can work with both of these databases. Initially a bit more work to get your system running, but it scales a (whole) lot better.
Use PostgreSQL as open source alternative, which has a feature-set similar to Oracle database. As I am not that familiar with MS-SQL I cannot say if the PostgreSQL feature-set is also similar with that product.