There are several database solutions for Linux, in fact above and beyond just databases there are SQL servers, both free and open source, and proprietary and expensive. I am very fond of two free and open source SQL server database systems. They is PostgreSQL and MySQL. There are plenty of web based graphical front ends for both and there are some X based graphical front ends (although like most things I prefer not to use graphical front ends for any of my database work).
For PostgreSQL and MySQL you can use webmin for a nice web based graphical database administration tool. For PostgreSQL I there is an Xwindows (tk based if I recall) utility called "pgaccess" that gives you an MS Access like graphical environment. Then of course you can run the expensive SQL servers like Sybase and Oracle and IBM DB2 on Linux and there are plenty of graphical administration tools for them for administration, even from a Windows client (much like MS SQL Server Enterprise Manager).