I was looking for a hierarchical database management system and the only one i came across was IBM's ims.Are there opensource systems that one can use?.
Since XML databases are hierarchical, you could look at those. I recently used BaseX and liked it a lot.
I found mumps and its GPL licensed.*Mumps (also referred to as M) is a general purpose programming language that supports a unique, hierarchical (or multidimensional) database facility * http://cs.uni.edu/~okane/mumps.html
In terms of hierarchical, it stores "documents" instead of "records" in "collections" instead of "tables". Using JSON, it's easy to create objects that represent hierarchical data. It also supports indexing and querying "into" these documents.
If you're thinking of XML databases, JSON should be competitive.
It is not open source, but Microsoft SQL 2008 Management Studio Express is free and allows XML datatypes starting with SQL Server 2005. If you are not familiar with using the XML datatype to store heirarchies, I am currently reading a book by Michael Coles called Pro SQL Server 2008 XML which introduces using XML in SQL.