Is it possible to create a connection to a MySQL database in ArcGIS 10?
If all you need is the tables of IDs, text, numbers (no geometries), then your best option is to use ODBC. You can install a MySQL ODBC driver for your system: http://www.mysql.com/downloads/connector/odbc/ download "Windows (x86, 32-bit), MSI Installer". (ArcGIS is still a 32-bit program, even on a 64-bit computer, so you will always require a 32-bit driver to match).
Then create a DSN for your database, here are some instructions for MySQL. If you are on a 64-bit computer, you need to ensure that you are using the 32-bit version of "ODBC Data Source Administrator", which is found at
Once you have successfully created and tested the DSN connection, you can add it to ArcGIS. In ArcCatalog, go to "Database Connections", "Add OLE DB Connection". Choose "Microsoft OLE DB Provider for ODBC Drivers", and you should be able to find your DSN under the "Use data source name" dropdown list. Test connection, and you should be good to go. You can join these attributes in ArcMap to other features using common IDs, etc.
However, geometries from the Spatial extension will not come through to the GIS. You would probably need to export these as another spatial format recognized by ArcGIS.