I like this thread idea, @Tom153.
Types of Pets: In an attempt to limit types to well-behaved, I warn in my house rules that nervous dogs will have a terrible time in our woods. Nervous dogs do have a lousy time, and they make the worst messes. Well-trained dogs not only have a good time, but are a lot of fun. We've had no other pets than dogs arrive. One set of guests told me they left their albino boa constrictor at home. Grateful shudder.
Best Practices: It can be muddy here. I leave handy in a box some old towels that can be used for wiping paws.
Fees: I do wish that adding a small pet fee was as easy as adding another person, that it was just a matter of the guest clicking 'number of pets in party' and the extra $10 or whatever appearing in the price breakdown. Pets ARE more work, even when they are nice. I dislike that it is a Resolution Centre matter, and unclear. I don't dislike it enough to turn to Host Voice.
Stories: One guest arrived with a surprise dog, and told me "I was going to mention him to you, then I thought, 'He deserves a holiday too,' so I didn't." Most dog stories here are non-stories: just good dogs being delightful.
Liability: Yikes. I like not to think of what will happen if a coyote or owl eats a guest's pomeranian. Is that what you meant by liability?
Enjoyed the other responses, and looking forward to more!