One thing that always bugs me is the impact of pets on wildlife. Taking dogs into wilderness areas can disrupt wildlife in a lot of ways. Wild animals will react to the predator scent of a dog by hiding and changing their routine - this might keep them from getting the food or water they need, or keep them from approaching their home, tending to their young, etc. I know dog owners want to take their pets everywhere they go but there are some places where domesticated dogs just don't belong.
As for cats, they stick closer to home, but they are voracious killers. They can eliminate bird populations and kill migratory birds that are passing through. I keep my cat indoors most of the time, and she's got a little bell on her collar (probably wouldn't do much good to keep her from stalking but it's something). Since cats are completely comfortable as inside pets, probably the best thing is to keep them inside (I'm not a fan of declawing).