Magnet in the generator?
Depends on the type of electrical machine.
All electrical machines can operate as Generators &amp; Motors. 

An electrical machine is an electrical &lt;-> kinetic energy converter which utilises magnetic fields. The real question is by what means does the stator &amp; rotor generate its magnetic field. 

Types of electrical machines

Brushed DC


Stator: Wound or permanent magnet 
Rotor: wound


Induction Machine


Stator: Wound
Rotor: Wound


Synchronous machine


Stator: Wound
Rotor: Wound or permanent magnet


Brushless DC or AC (these are sync machines)


Stator: Wound
Rotor: Permanent magnet 


Switched Reluctance


Stator: Wound
Rotor: neither


This is ignoring inside out machines. 

For higher power generators however, national grid type machines, the topologies of these machines are wound rotor synchronous machines