The choice of an alternative to Access, Gromit, might depend upon what it's to be used for.
Many (most?) businesses seem to use Excel for many purposes that would logically seem to require database software, rather than a spreadsheet program, but still remarkably successfully.
If an alternative desktop-based relational database is needed though, OpenOffice Base is well up to the job.
However the majority of people who use Access these days seem to be developing web apps and FileMaker Pro might well be the way to go.