I guess it is more about what you want to wear. As has been said, things are pretty casual in that regard. That being said, I wouldn't wear a pair of dress shoes with a pair of faded, ripped up jeans. Of course I don't wear ripped up jeans at all.
In truth I generally match the shoes more to the type of shirt I'm wearing with my jeans (keeping in mind that all of my jeans are "nicer"). If it is a button up shirt I'll wear lace up shoes or possibly loafers. If it is a polo, I wear loafers. If it is a more casual short like a t shirt or at least one without a collar I will wear a pair of Cole Haans, Sketchers, or even Doc Martens. And yes, I know ALL of shirts have collars unless you've ripped them off but I'm talking about not having fold over collars instead of the flat ones.
Running shoes and the like I generally leave for workout clothes.