I have some portals that show only the existing records from a particular table.

Then in another portal it shows existing records (different table/different portal/different layout), however it also shows a blank row for a new record below the existing records. If I click a check box in that row it makes yet another record... This is not ok - how do I stop this?

You'll have to change the relationship that portal is using. In the Edit Relationships window, uncheck the box on the related table's side that says "allow creation of records in this table via this relationship."

That feature is quite useful when you don't want your users to have to click a "create new" button to add a new row in the portal, but you can turn it off easily enough.