Are there any object databases for .NET or with bindings for .NET?
Intersystems Caché also has a managed .NET provider - can't speak from experience about its quality and usability, though:
http://www.intersystems.com/cache/technology/components/net/index.html
Marc
Wikipedia lists some.
You could also consider using Bamboo.Prevalence - a .NET persistence engine similar to Prevayler for Java. That is not a database in a usual sense (more on this here), but could be appropriate in some cases.
Majority of object databases are not really .NET databases, as they are written in Java, and then converted into .NET (C#) by some kind of converter. That results in really poor performing code.
You can look into Eloquera Database, which is pure .NET-based object database with SQL, and performing from 10 to 1000 times faster than db4o.
Take a look at 100% .NET object database - siaqodb ( http://siaqodb.com )
Databases for .NET are also listed in SharpToolbox.com's DBMS category.
You'll find object databases in there.