Depending on the intended use, there are a number of database architectures in use. Many databases use a combination of strategies. On-line Transaction Processing systems (OLTP) often use a row-oriented datastore architecture, while data-warehouse and other retrieval-focused applications like Google's BigTable, or bibliographic database (library catalogue) systems may use a Column-oriented DBMS architecture.
Document-Oriented, XML, knowledgebases, as well as frame databases and RDF-stores (aka triple-stores), may also use a combination of these architectures in their implementation.
Finally, it should be noted that not all databases have or need a database 'schema' (so called schema-less databases).
Over many years the database industry has been dominated by General Purpose database systems, which offer a wide range of functions that are applicable to many, if not most circumstances in modern data processing. These have been enhanced with extensible datatypes, pioneered in the PostgreSQL project, to allow a very wide range of applications to be developed.