how would our bodies react if we only ate canned food?

Actually, many canned products have as many or more nutrients as fresh because the vegetables and fruits are packed in the cans very close to the production area and at the peak of nutrition. They are then sealed and cooked, so all the nutrients stay in the can. While some nutrients are destroyed by the heating process, so are all of the bacteria. Fresh products often have a bacterial load. Therefore, your body would react to the canned goods just like they react to any other food. As long as you ate the proper variety of canned food you wouldn't have any adverse effects.

I don't think we'd feel too good, canned things are pretty devoid of nutrients compared to fresh because they have been cooked until mushy and then on top of that have been sitting around for who knows long. My guess is that long term, nutrient deficiencies would develop. Also the aluminum from cans can leech into the food. Blech...

Fresh>Frozen>Canned