Just a walk: 6' leash of some sort (Zumi or Bold Lead right now), harness (generally an Xtra Dog one). A few poop bags in my pocket.
Short hike (less than 2 hours): 6' leash or Flexi, harness as above, small lumbar pack with dog treats, poop bags, and my phone, maybe a water bottle if it's hot.
Long hikes (up to 6 hours currently): 6' leash or Flexi, dog back pack (Granite Gear or Ruffwear) with collapsible bowl, dehydrated raw patties in a ziplock, poop bag dispenser, extra slip lead, and two 0.6L Platypus soft water bottles. My Osprey hiking pack with my 2L water bladder, first aid kit, rain gear (pants and coat if likely, just a poncho if not), extra pair of socks, snacks/lunch, map, cell phone, limited survival gear (matches, emergency blanket, compass).