Summing up the discussion in the comments emphasizing the experimental aspect:
The number of fields depends on the theoretical model, because they are theoretical postulates on the quantum field theory that separates the particular model from all others.
In the standard model of particle physics, which is the one that encapsulates all particle data up to now, the fields on which operators operate are the fields of all the particles in the table..
GUT will have more fields, as will supersymmetric theories.
One has to keep in mind that any theory that aims in describing data and observations should have the standard model as a subset or embedded. If or when a supersymmetric particle is discovered at the LHC then the number of fields will have to expand according to a new standard model.