Wikidata offers copies of the available content for anyone to download.
There are several different kinds of data dumps available. Note that while JSON and RDF dumps are considered stable interfaces, XML dumps are not. Changes to the data formats used by stable interfaces are subject to the Stable Interface Policy.
JSON dumps (recommended)
This is the recommended dump format. Please refer to the JSON structure documentation for information about how Wikidata entities are represented.
Hint: Each entity object (data item or property) is placed on a separate line in the JSON file, so the file can be read line by line, and each line can be decoded separately as an individual JSON object.
Note that the files are using parallel compression, which means that some decompressors cannot reliably unpack the files. If you are using Windows you can use e.g. Bzip2.
JsonDumpReader is a PHP library for reading the dumps.
First, canonical RDF dumps using the Turtle format can be found under https://dumps.wikimedia.org/wikidatawiki/entities/. The mapping is described here. These full statements are noted as all.
Secondly, so called truthy dumps are provided. They use the nt format. They are in the same format as the full dumps, but limited to direct, truthy statements. Therefore, they do not contain meta data such as qualifier and references.
The Wikidata Toolkit project also provides RDF dumps, using a slightly different mapping. These dumps can be found at http://tools.wmflabs.org/wikidata-exports/rdf/. The RDF mapping used by the Wikidata Toolkit is described in the paper Introducing Wikidata to the Linked Data Web.
The complete dumps together contain all entity information in Wikidata with the exception of order (of aliases, of statements, etc.), which is not naturally represented in RDF. Simplified dumps encode statements that have no qualifiers as single RDF triples (references are omitted).
Warning: The format of the JSON data embedded in the XML dumps is subject to change without notice, and may be inconsistent between revisions. It should be treated as opaque binary data. It is strongly recommended to use the JSON or RDF dumps instead, which use canonical representations of the data!
Old JSON and RDF dumps
Old RDF and JSON dumps can be found on the Internet Archive (Q461):
The data model can be looked up here. The data model describes the fundamental building blocks of Wikidata's data.
An overview over the schema of the database can be found at this page. (This is not the schema of the data in Wikidata.)