Here's a shared hosting provider im testing atm,
www.register365.ie , no limit on the number of databases only limited to the size of quota. it is an IIS server or Apache server depending on the OS of your choice. both are €4/month for the basic package.
Unlimited MySQL Databases & Users
Unlimiited PgSQL Databases & Users
Unlimited MS SQL Databases & Users
250MB MySQL Quota
250MB PgSQL Quota
250MB MSSQL Quota
PhpMyAdmin & Remote Direct Access
PgMyAdmin & Remote Direct Access
MS SQL Web Based Enterprise Manager
Full DSN/ODBC Management