I used to use Nike running or cross training (40-50 at Kohl's or Sports Authority) but it would irritated my arches. So I switched to Under Armor running shoes when they came out and found relief some relief for my arches, but they are too soft for bike riding. I'm clipless now and probably won't go back.
I have a pair of Shimano mountain bike shoes and pedals for my commuter/beater.