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Is there is a study or classification available on different types of databases? (Examples include structured, unstructured, semi structured relational, object oriented, folksonomies, etc.)

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One of the key differences between the different paradigms for data management is the underlying structure used to bind pieces of data together. IMHO, the difference between structured, unstructured, semi-structured is not precise enough : the point is that the underlying structure may be more or less flexible. This formal structure is used to define the semantics of the model and so it drives everything: the query language, the concrete (in memory, on disks) data-structures, the graphical representation etc.

In the standard relational paradigm, the core concept is that of a tuple (in the set theoretic sense). XML variants are clearly tree based, RDF related models are grounded on labelled directed multi-graphs: those three models are examplified in this recent draft paper. Nowadays, one talks about stream data models grounded on infinite relations, key-values stores are grounded on functions/maps. I guess folksonomy may be multi-set oriented etc.

So "the study of different types of databases" may turn out to be "the study of formal data-structure useful for large data management".

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Wikipedia has a list of database models: http://en.wikipedia.org/wiki/Database_model

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