[database] What database does Google use?

As others have mentioned, Google uses a homegrown solution called BigTable and they've released a few papers describing it out into the real world.

The Apache folks have an implementation of the ideas presented in these papers called HBase. HBase is part of the larger Hadoop project which according to their site "is a software platform that lets one easily write and run applications that process vast amounts of data." Some of the benchmarks are quite impressive. Their site is at http://hadoop.apache.org.