GemStone is a common one, but object databases are not very common due to the maturity, efficiency, and predictability of relational databases. The deep pipelining and caching models of CPUs are a better match for RDBMs than object ones.
I understand that Gemstone is an Object-Oriented Database that stores objects and is great at that. But can you query those objects with SQL?
What I'd like to understand is, is there some basic reason why RDBMS and ODBMs must be different databases. Or could their conceptual models of data perhaps be generalized into a single model. Using hyper-graphs perhaps. :-)
https://en.wikipedia.org/wiki/Gemstone_(database)