What is an "Obsolete" Database?
Depends on who you ask.

Is it in terms of new features, etc.? For example, a 32-bit RDBMS system could be considered obsolete nowadays, because 64-bit is common, and most engines run safely on a 64-bit platform, with access to more memory.

Is it in terms of scaling? For example, an old design that doesn't scale well, might be considered obsolete.

A database with queries that use old-style joins, could be considered obsolete, and in this case would prevent upgrades to newer technology without changing the code.

Some wonks like to say that SQL itself is obsolete, that NoSQL technology is better suited to certain problem areas like unstructured data. I personally wouldn't say this is the right use of "obsolete", but that could be an example too.