I've worked with CODASYL network databases, which are essentially the same as object databases (except no storage of methods in the database, which most OO databases don't do either).

Pros: - very fast for queries/updates along the designed network paths.

Downsides:

- not necessarily fast if network path is complex,

- proprietary API,

- corruption can be difficult to impossible to fix,

- corruption _does_ occur,

- depending on data structures used, DB may need re-organization (resizing),

- design requires skill: not easy to redesign or modify once deployed.

While fun to work with, I would hesitate to recommend using such a database unless absolutely necessary. Relational databases are much easier to set up, reconfigure, query and update. These characteristics alone usually preclude the use of an object database.