Yes, dogs are allowed in many U.S. national parks, but federal rules limit where they can go and require them to be leashed or otherwise confined at all times.
Under National Park Service regulation 36 CFR 2.15, a pet must be crated, caged, physically confined, or kept on a leash no longer than six feet. Pets are banned from public buildings, public transportation vehicles, and designated swimming beaches, and each park superintendent can close additional structures or areas to pets, which is why trail and campground rules differ widely from park to park. Owners may not leave a pet tied to an object and unattended except where a park allows it, must follow the park’s waste-disposal conditions, and can be cited if a pet’s barking or howling is unreasonable or frightens wildlife. Guide dogs and hearing dogs are exempt from the building, vehicle, and beach ban. Pets found running loose can be impounded, with the owner charged for boarding, feed, and veterinary costs, and an unclaimed pet may be put up for adoption after 72 hours. Check the individual park’s pet rules before you go.
Source: Electronic Code of Federal Regulations, 36 CFR 2.15 (Pets), National Park Service
Image: Visitor with a leashed dog at Hoh Campground, Olympic National Park, NPS photo by D. Archuleta, public domain, via Wikimedia Commons.