One
list of GMO crops [in the USA] says "The 10 genetically modified crops available today: alfalfa, apples, canola, corn (field and sweet), cotton, papaya, potatoes, soybeans, squash and sugar beets." Field trials of other crops are happening around the world, but I don't see blueberries or blackberries mentioned in any of the lists google gave me.
This article tells you how to avoid GMO products [in the USA].
Wikipedia is very clear too.