If I don\'t need a primary key should I not add one to the database?
That depends very much on how sure you can be that you don't need one. If you have just the slightest bit of doubt, add one - you'll thank yourself later. An indicator being if the data you store could be related to other data in your DB at one point.
One use case I can think of is a logging kind-of table, in which you simply dump one entry after the other (to properly process them later). You probably won't need a primary key there, if you're storing enough data to filter out the relevant messages (like a date). Of course, it's questionable to use a RDBMS for this.