Kubuntu no longer ships with a default database application, however you have options in which to choose from.
OpenOffice.org Base is the database application created by the same group that creates the OpenOffice.org suite. OpenOffice.org Base is in the Main repository. Please refer to the Adding Applications documentation for help on installation.
Kexi is also a choice for a database application. Kexi is part of the KDE KOffice suite and tends to integrate better within KDE. Kexi is in the Main repository. Please refer to the Adding Applications documentation for help on installation.
It is recommended you try both applications in order to see which one works best in your situation.