BergDB is a light-weight, open-source, NoSQL database designed from the start to run ACID transactions. Actually, BergDB is "more" ACID than most SQL databases in the sense that the only way to change the state of the database is to run ACID transactions with the highest isolation level (SQL term: "serializable"). There will never be any issues with dirty reads, non-repeatable reads, or phantom reads.
In my opinion, the database is still highly performant; but don't trust me, I created the software. Try it yourself instead.