This is one of those issues that people "never care about until they need it". A large number of database driven websites have databases almost excusively read-only (eg writes only happen when the admins update content, and 99% of the transactions are reads / SELECTs by viewers). In those cases, you can probably safely schedule backups on simpler databases (MySQL) and keep the database online without worry (scheduling backups away from when admin INSERTs etc are being done).
For MySQL databases, there are some other proven approaches. Replication was mentioned above, but the biggest advantage of having a "slave" database server with an exact copy of the "master", is that you can drop the slave offline whenever you like, and make backups from it (avoiding the integrity problems).
Great article on this approach
here !
PostgreSQL has a few approaches under continuing development, but some with rough edges still.