Thoughts: I also did not see a relational database system that includes the concept of branching ... although the concept itself seems to be very useful IMHO.
I know that Microsoft Team Foundation Server + Visual Studio 2010 (Premium or Ultimate only) has database integration with source control through Database Projects. I am sure that other version control systems have similar capabilities ... but this does not answer your question for a lightweight or integrated database version control system. (Therefore, this is technically not the answer - just some kind of information that can help you solve your basic question).
A quick search found some useful articles, but didn't seem to exactly answer this query:
RedGate is a top-level database developer company that develops solutions for Microsoft SQL Server, Oracle, and possibly other database solutions. The trick is that RedGate SQL Source Control 3.0 allows you to work with your version control system in SSMS (Microsoft SQL Server Management Studio), but it is not DB VCS (version control system) on its own. Excerpt from their website:
SQL Source Control is an add-on for SQL Server Management Studio that allows you to get the database into source control. SQL source code management therefore brings the benefits of change management and source collaboration for database development without affecting the workflow or requiring new development processes. Note. Source SQL Control is not a version control system; it allows you to store your databases in your existing version control system.
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