OODBs are different from Relational database in that they store data objects, rather than records. OODBs have been around for a while, but have not really caught on. People in the industry believe that as technologies such as XML become more and more widespread, OODBs will become more appealing.
Also take a look at Versant's Web Site, which lists case studies of some of their clients.

Other vendors include ObjectStore, Objectivity/DB and Poet, which are reviewed in an article entitled "Choosing the right OODB Solution".

The OODBMS Facts website's FAQ lists some good examples of companies using them.
From the FAQ:
If you, as an individual investor, trade stocks over the Internet, there is a good chance your trades go to the Chicago Stock Exchange and are traded in a Versant ODBMS. Radio Computing Services is the world's largest radio software company. Its product, Selector, automates the needs of the entire radio station -- from the music library, to the newsroom, to the sales department. RCS uses the POET ODBMS because it enabled RCS to integrate and organize various elements, regardless of data types, in a single program environment.

The NeoAccess ODBMS is used in the Encyclopedia Britannica and the Family Tree Maker. The Objectivity/DB ODBMS is used as a data repository for system component naming, satellite mission planning data, and orbital management data deployed by Motorola in The Iridium System.

The ObjectStore ODBMS is used in SouthWest Airline's Home Gate to provide self service to travelers through the Internet. This allows them to plan trips and purchase tickets on SouthWest Airlines.

Ajou University Medical Center in South Korea uses InterSystems' Cach� ODBMS to support all hospital functions including mission-critical departments such as pathology, laboratory, blood bank, pharmacy, and X-ray.

West McLaren Mercedes, developer of the MP4/13 Formula One racing car, is using Computer Associates' Jasmine ODBMS to enable its engineers to effectively monitor and track its Formula One car's performance.