While the Intelligence Ministry may only train as many spies as it has levels, it is possible for it to control spies far in excess of its level. Some players have hundreds of spies in the Intelligence Ministries. There are a few methods of doing this but probably the easiest and the most comonly used is running the Incite Mutiny mission on another empire's planet.
**Because of the new spy changes this option is no longer available.
The burn option in the Intelligence Ministry allows you to fire one of your agents. In order to downgrade your Intelligence Ministry you will need to have fewer spies than the level of the Intelligence Ministry. The Burn option also has a small chance of causing the spy who was burned to join the planet that he was burned on.
You can train your existing spies via the Intel Training Facility, Mayhem Training Facility, Politics Training Facility, and Theft Training Facility. Training via these buildings do not count toward retirement.
*Should you lose control over one of your planets the spies that controlled by that planet will instead be controlled by your Capital Planet.