Within reason, of course. My pedals are no Straitlines (they're Flatboys, if you're wondering), but they just don't work very well when your shoe's sole isn't very flat. My running shoes don't stick well, and I'd imagine a lugged hiking shoe is even worse. Conversely, I wear Five-Ten Impacts and they're awesome, but they're not going to work well with those cheap pedals you get on entry level bikes that don't have pins.

Also, I second what Cryptid said. Stiffer sole, sticky rubber, and to add to that, a flat sole (which any skate or bike shoe will give you, though bike shoes will do a better job with the stiff sole, and Stealth rubber is hard to beat.