While we (Research & Data @ WMF) consider maintaining a standard dump of categories and pagelinks, anyone can pull such a dataset from tool labs slaves (see
http://tools.wmflabs.org) with the following two queries.
/* Get all page links */
SELECT
origin.page_id AS from_id,
origin.page_namespace AS from_namespace, origin.page_title AS from_title,
dest.page_id AS to_id, /* NULL if page doesn't exists */
pl_namespace AS to_namespace,
pl_title AS to_title
FROM pagelinks
LEFT JOIN page origin ON origin.page_id = pl_from
LEFT JOIN page dest ON dest.page_namespace = pl_namespace AND dest.page_title = pl_title;
/* Get all category links */
SELECT
origin.page_id AS from_id,
origin.page_namespace AS from_namespace,
origin.page_title AS from_title,
cl_to AS category_title
FROM categorylinks
LEFT JOIN page origin ON page_id = cl_from;
Note that these tables are very large. For English Wikipedia, pagelinks contains ~900 million rows and categorylinks contains ~66 million rows.
-Aaron