To me it looks like XML file structure, so I would consider
using XML database (probably native one like Xindice).

You can find a list of XML database at
http://www.rpbourret.com/xml/XMLAndDatabases.htm
or somewhere around ;)

The most straight forward way would be to store data in a normal sql
database.

One table for the hierarchy

create table dir
(
dir_id number,
parent_dir_id  number,
dir_name varchar2(255),
dir_type number,
dir_metadata varchar2(255)
)

create table file
(
file_id number,
dir_dir_id number,
file_type number,
file_metadata varchar2(255)
)

Then you have a hierarcy defined in the table dir, and each file belongs
in exactly one dir (unless you make a N:N relationship ofcourse). You
could also store information about type and metadata in separate tables
or whatever suits your needs.

Next would be to select a persistence technology. This would work with
most known technologies and the easiest would probably be to use the
same as you use for other relational data in your application. Straight
jdbc, Hibernate, CMP ... it's your choice. CMP has some features to
manage relations automatically for you, and I'm sure Hibernate has some
features to help you out with the relational/hierarchical stuff here as
well.

This method would give you all the pros and cons that sql databases
always do, transactions and so on. I don't know how you intend to use
your hierarcy so it's impossible to tell if this is useful for you.

One alternative for storing hierarchical data that sometimes comes up is
using Prevayler (you'll find it at google), which is sort of a very fast
in-memory hierarchical database. I've never tried it, but it's
supposedly very fast, and has different characteristics from a normal,
relational dbms.