I have regular homeowner's insurance. What type(s) of insurance should I get? My concerns are: 1) the dog runs away (even if I have it on a leash), 2) another dog attacks "my" dog unexpectedly as we are walking, 3) a dog breaks something in my house, etc.
Here is the description of the insurance provided by Rover:
https://www.rover.com/insurance/
Injuries to the Rover dog are covered, injuries to your own pets are covered provided they were the direct result of the Rover dog. Damage to your personal property is not covered (though it should be covered by your homeowner's insurance). I don't think there is any insurance option that would cover the loss of a dog in your care.
No.1 is not covered by any provision of Rover's insurance or Terms of Service. No. 3 is covered by your homeowners. I'm not sure who "my" dog is. If your dog bites the guest dog or vice versa, then Rover's insurance. Remember though, with all insurance, there are deductibles, even Rover's. Also, nothing would prevent a client from suing you for loss of their dog.
Rover's insurance does cover the resident dog, if injuries are caused by the Rover dog - "Coverage for Sitter's Resident Pets: This coverage is valid for veterinary care for the sitter's resident pet(s) as a direct result of contact with the pet parent's pet. Up to $5,000 for the sitter’s pet(s); $250 deductible per incident, covered by the sitter"