Yes, the blackberries come up on canes and can be either thorned or thornless. There have been a lot of different cultivars of thornless blackberries that have been developed with various plant characteristics.
I have one thorned variety, Kiowa, which can grow some viscious thorns, but the berries are huge and it is a vigorous producer. I have had some of these berries 1 1/2 inch long and weighing an ounce a piece. But, because I have small children, I will be moving these out of the garden into a remote part of the yard.
I grow the Triple Crown thornless blackberries and tie them to trellises. They are supposed to be one of the best for size, flavor and yield, So far they have been decent producers and the fruit is great, this will be their third year. I have read that 8 year old plants have produced 50 pounds per plant (my guess under ideal conditions). I will be putting in two additional varieties of thornless, Arapaho and Ouchita, once my order gets here. I have heard a lot of good about these as well so we will see. I always like to see what a different cultivar has to offer!
David