Well, I don't know what a hackberry is, but when I was a kid, I used to climb up in our mulberry tree and eat the berries. I loved them. That was a long time ago, but I remember them as being very sweet, at least if they were ripe.
It's a tree that grows on a runner, like grass does. They're almost impossible to eradicate, and happily grow right out from underneath anything in their way. (Like your house)
In fall, tons of tiny mauve berries that the birds love, and for some reason, our dogs like to eat the ones the birds drop. (Why do we always seem to have the weird pets? :)
We did try eating the mulberries the first year we were here. I honestly wasn't all that impressed, but for all I know, the tree could be an ornamental variety. The berries were tiny and kind of sour.
The best jam and jelly can be made from mulberries. Use the blackberry receipe on the Sure-Jell box.
Wild Mexican plums are even better. It takes 5 pounds to make a batch (Sure Jell plum receipe) which equals a lot of walking here, but worth it. It's the best plum jelly ever--plum with an exotic overtone.
Prickly pear (the magenta fruit only)is the best, but a bit tricky. Tastes like a cross between crabapple and watermelon. Many years mine fails due to having to pick the fruit at just the right time. Too ripe will not jell, but it's still fabulous pancake syrup when that happens.