Yes - PostgreSQL.
I've used it (starting several years ago) for mission-critical RDBMS support. It HAS transactions (real ones) and referential integrity, and is considered a "mainstream" product that is under the open source (BSD license) model.
In fact, I wrote my former ISP's billing, authentication, user logging and other "subscriber data" systems around it using a custom character-interface model, all from "C".
It is my personal preference for an RDBMS when you simply can't afford to have things go "boom." We had over 30GB of online data in the system (we kept literally every single session log - I could tell you when you were on, how many bytes you transferred, from what phone number you dialed (from the ANI), etc - going back to the inception of the company.) It survived several hardware failures over a number of years without ANY data corruption.
In the last couple of years online replication has become available which makes it even nicer for enterprise applications; its the "base" upon which the AKCS package will run, if I ever get it done
All the "common" tool interfaces are there for it as well - I know PHP is supported, and I think Python, Perl and a few others are as well, along with a "C" and C++ interface. I'm very familiar with the "C" interface; its bomb-proof.
I've got several "major" applications running on it now, from a boat listing database (kinda like Yachtworld, but as a project I'm working on) to a political advocacy fax-server system (matches web petitions to reps and senators, and generates faxes, etc), to the AKCS project, along with a number of others.
I have
never (in over six years of use) had it go out from under me. Not once. That's quite an accomplishment, as I tend to hammer the bejeezus out of the products I use.
You don't even want to get me started on commercial products like Oracle and Sybase...... what I have to say about most of them is not fit for polite company.
The problem with most packages like vB is that they depend on some of the "quirks" in the implementations of their base technology to work, which is why they don't specify "Any SQL database with PHP front end", but rather get quite a bit more specific......
(I'm not a PHP, Perl, or other similar "tool" fan either. Too many problems going that route. IMHO those tools encourage bad design by shortcutting the design process that should go into a product, and the overhead is unnecessary. I write nearly
everything that I do in "C" and have for many years..... before that, most of my work was in some version of assembler!)