This is quite an important one for people doing mouse work, though it is important to note that JAX offer Mart and Batch-Query functionality through the web site as well which may well suit many peoples needs.
Unison is a comprehensive set of protein sequences with lots of precomputed results of many types. Unison was designed primarily for rapid mining of complex combinations of protein features. There's a simple homology-based structure viewer that can map SNPs and arbitrary regions onto structures.
The Unison source and website were released under the Academic Free License, and the data are released under the Creative Commons. There's a public PostgreSQL service (Try 'psql -h unison-db.org -U PUBLIC -d unison'). Command line tools are available. Loading and computing are automated and incremental, and coordinated by a makefile.
Not really MySQL databases but next to proper SQL access there are quite a few datasources out there that are accessible through REST/SOAP. Many of these sources are listed on http://www.biocatalogue.org/.
I am afraid that is not completely correct ....
Ensembl up to version 47:
Ensembl up from version 48 onwards:
Ensembl BioMart up to version 47:
Ensembl BioMart from version 48 onwards:
See also: http://www.ensembl.org/info/data/mysql.html