If I don\'t need a primary key should I not add one to the database?
Well...
Each table in a relational DB needs a primary key. As already noted, a primary key is data that identies a record uniquely...
You might get away with not having an "ID" field, if you have a N-M table that joins 2 different tables, but you can uniquely identifiy the record by the values from both columns you join. (Composite primary key)
Having a table without an primary key is against the first normal form, and has nothing to do in a relational DB