You can create small, locally accessible databases with Microsoft Access. It easy to use and has the same look and feel as other Microsoft Office products.
Access stores an entire database application within a single file which may contain tables and queries, as well as application objects like forms and reports.
For multi-user and shared databases you may register to use MySQL:
These services are available for staff and academic research users who need the extra processing resources of an enterprise system.
For example, the ArcGIS SDE component links to the Academic Oracle service for registered users of that service, as do Geomatica and GRASS.