I’ve used ZODB for more than ten years now, in Zope and outside. It’s great if your data is hierarchical. The largest data store a customer operates has maybe. I don’t know, 100GB in it? Something on that order of magnitude anyway.
Here is a performance comparison against Postgres.
If you’re writing a WSGI web app, these packages may be useful:
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repoze.tm2 (docs)
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repoze.zodbconn (docs)