Wikidata offers copies of the available content for download. These databases can be used for personal or commercial use, backups or offline use. All structured data from the main and property namespace is available under the Creative Commons CC0 License. Text in the other namespaces is available under the Creative Commons Attribution/Share-Alike License; additional terms may apply. Media items and other content are available under other licenses, as detailed on their description pages.
Full XML dumps of Wikidata can be found at http://dumps.wikimedia.org/wikidatawiki/.
JSON dumps containing all Wikidata entities as a list can be found at http://dumps.wikimedia.org/other/wikidata/. Those are being created on a weekly basis.
Note that there are also several other methods for accessing structured content from Wikidata, which may not require a complete database dump.
Incremental dumps (or Add/Change dumps) for Wikidata are also available for download. These dumps contain stuff that were added in the last 24 hours, reducing the need of having to download the full database dump. These dumps are considerably smaller than the full database dumps.
These dumps are available here.