I found out that if the tables in the database I am trying to generate a Model for, do not have a Primary Key defined on one of the columns, the EF will not be able to generate classes for the tables in that Database.
The Tutorials that I was walking through for learning MVC using EF did not mention this point.
So this was an important discovery I made and thought I might share with it others who may experience the same problem, in case they are new to EF.