What's a good word for displayed non-frozen non-canned vegetables in the grocery store?

Solution 1:

In a supermarket it's generally described as the "produce section"

Solution 2:

For me, fresh vegetables mean not treated for long preservation (canned, frozen, dried or else), and not freshly harvested. (Well, I do hope that there is some kind of correlation, at least in the places where I buy mine.)

In addition, the New Oxford American Dictionary has:

(of food) recently made or obtained; not canned, frozen, or otherwise preserved.

which appears to back my own usage.

Solution 3:

Definition of fresh:

7. not preserved by freezing, canning, pickling, salting, drying, etc.: fresh vegetables.

Though it also implies other meanings such as freshly harvested as you mentioned. If you don't want these implied meanings, you need to physically write "non-frozen" "non-canned" in order to be clear.