Here are the most commonly used City animal laws (not all inclusive) and the most pertinent for pet owners to be aware of. For the complete Hampton City Animal Code refer to this link.

Sec. 5-37. Dogs and cats deemed personal property; rights relating thereto. All dogs and cats shall be deemed personal property and may be the subject of larceny and malicious or unlawful trespass, and the owners thereof may maintain any action for the killing of such dogs or cats, or injury thereto, or unlawful detention or use thereof, as in the case of other personal property.

Sec. 5-38. Running at large.

(a) Dogs.
(1) It shall be unlawful for any person to permit any dog owned or kept by him to run or go at large within the city, whether such dog is licensed or not.
(2) The first violation of this section shall constitute a Class 4 misdemeanor. The second violation on the same animal shall constitute a Class 3 misdemeanor and subsequent violations on the same animal shall constitute a Class 2 misdemeanor. Any owner cited for three (3) violations of this section, may have his animals impounded or spayed and neutered at the owner's or custodian's expense.
(3) A violation of this subsection (a) shall constitute a Class 2 misdemeanor if the dog, while at large within the city, attacks a human being or another animal without provocation.

(b) Cats.
(1) It shall be unlawful for any person to permit any cat owned or kept by him to run or go at large within the city unless the cat is spayed or neutered and properly licensed in accordance with Article IV, sections 5-51 through 5-60 of the Hampton City Code.
(2) However, it shall be unlawful for any person to permit any cat owned or kept by him to run at large if said cat habitually causes destruction or damage to the property of another or habitually creates a nuisance.
(3) The first violation of this section shall constitute a Class 4 misdemeanor. The second violation on the same animal shall constitute a Class 3 misdemeanor and subsequent violations on the same animal shall constitute a Class 2 misdemeanor. Any owner cited for three (3) violations of this section, may have his animals impounded or spayed and neutered at the owner's or custodian's expense.
(5) Cats identified as part of a managed feral cat colony in accordance with the provisions of section 5-43 shall be exempted from the requirements of section 5-38(b)(1) only.

Sec. 5-39. Female dogs and cats in heat.

No person shall permit any female dog or cat in heat to go at large in the streets or remain on his premises to the annoyance of the neighborhood. Each day that a dog or cat is allowed to remain on such person's premises to the annoyance of the neighborhood shall be considered a separate violation of this section.
(Ord. No. 735, § 4-15, 11-10-82; Ord. No. 1385, 10-13-04)

Sec. 5-41. Dogs riding in motor vehicles.

(a) It shall be unlawful and a Class 4 misdemeanor for any person who owns or has control of any dog to allow such dog to ride in any motor vehicle in any portion thereof that is open in such a manner as to permit such dog to jump out of the vehicle or to be thrown there from by acceleration of, stopping of, or accident involving, such vehicle, including, but not limited to, the open bed of a truck, the interior of a convertible vehicle with the top down or removed, the rear storage portion of a station wagon with the tailgate open, the trunk or hatchback portion of any vehicle with the trunk or hatchback open. For purposes of this section, the operator of a motor vehicle shall be deemed to have control of any dog riding therein.
(b) The provisions of subsection (a) above shall not apply to:
(1) Any person who owns or has control of any dog and who allows such dog to ride in the prohibited portion of any motor vehicle if such dog is confined to a cage of adequate construction and design to prevent its escape therefrom.
(2) Any portion of a motor vehicle which is fully enclosed except for open windows.
(Ord. No. 1003, 3-27-91)

Sec. 5-42. Dangerous and vicious dogs.

(a) Terms defined. As used in this section, "dangerous dog" means a canine or canine crossbreed that has bitten, attacked, or inflicted injury on a person or companion animal or killed a companion animal, however, when a dog attacks or bites another dog, the attacking or biting dog shall not be deemed dangerous (i) if no serious physical injury as determined by a licensed veterinarian has occurred to the other dog as a result of the attack or bite or (ii) both dogs are owned by the same person. No dog shall be found to be a dangerous dog as a result of biting, attacking or inflicting injury on another dog while engaged with an owner or custodian as part of lawful hunting or participating in an organized, lawful dog handling event. "Vicious dog" means a canine or canine crossbreed that has (i) killed a person; (ii) inflicted serious injury to a person, including multiple bites, serious disfigurement, serious impairment of health, or serious impairment of a bodily function; or (iii) continued to exhibit the behavior which resulted in a previous finding by a court that it is a dangerous dog, provided that its owner has been given notice of that finding.
(d) Registration certificate and tag. The owner of any animal found to be a dangerous dog shall, within ten (10) days of such finding, obtain a dangerous dog registration certificate from the local animal control officer for a fee of fifty dollars ($50.00) in addition to other fees that may be authorized by law. The local animal control officer shall also provide the owner with a uniformly designed tag that identifies the animal as a dangerous dog. The owner shall affix the tag to the animal's collar and ensure that the animal wears the collar and tag at all times. All certificates obtained pursuant to this subsection shall be renewed annually for the same fee and in the same manner as the initial certificate was obtained.
(f) Confinement, leashing and muzzling. While on the property of its owner, an animal found by a court to be a dangerous dog shall be confined indoors or in a securely enclosed and locked structure of sufficient height and design to prevent its escape or direct contact with or entry by minors, adults, or other animals. The structure shall be designed to provide the animal with shelter from the elements of nature. When off its owner's property, an animal found to be a dangerous dog shall be kept on a leash and muzzled in such a manner as not to cause injury to the animal or interfere with the animal's vision or respiration, but so as to prevent it from biting a person or another animal.
(h) Notification of authority. After an animal has been found to be a dangerous dog, the animal's owner shall immediately, upon learning of same, notify the local animal control authority if the animal (i) is loose or unconfined; (ii) bites a person or attacks another animal; (iii) is sold, given away, or dies; or (iv) has been moved to a different address.
(i) Willful noncompliance deemed misdemeanor. The owner of any animal that has been found to be a dangerous dog who willfully fails to comply with the requirements of this section shall be guilty of a Class 1 misdemeanor.
(l) Evidence of liability insurance. All certificates or renewals there of required to be obtained under this section shall only be issued to persons who present satisfactory evidence that the owner has liability insurance coverage, to the value of at least one hundred thousand dollars ($100,000.00), that covers animal bites.
(n) Owner of companion animal entitled to recover damages. The owner of any companion animal that is injured or killed by a dog shall be entitled to recover damages consistent with the provisions of § 3.1-796.127 from the owner of such dog in an appropriate action at law if (i) the injury occurred on the premises of the companion animal's owner, and (ii) the owner of the offending dog did not have the permission of the companion animal's owner for the dog to be on the premises at the time of the attack.

Sec. 5-43. Unlawful care of feral cats.

(a) Any person intentionally providing food, water, or other forms of sustenance to a feral cat or feral cat colony must furnish a signed statement to the animal control officer agreeing to comply with the following conditions. Those persons who have furnished a signed statement to the animal control officer agreeing to comply with the conditions contained in this section are exempt from the requirements of Article IV of this chapter, entitled Dog and Cat Licenses.
(1) Annual registration with the animal control officer as a person caring for feral cat(s) or a feral cat colony. There will be no costs associated with this registration. The registrant shall be deemed the owner or custodian of the cat(s) for purposes of this chapter.
(2) Provide documentation of support by surrounding neighbors of proposed location for feral cat colony.
(3) Assure responsibility and arrangements for feeding and providing emergency veterinarian treatment as needed to the cat or cat colony regularly throughout the year, including weekends, holidays and vacations and in the absence of the caregiver.
(4) Regular and frequent trapping through use of humane box traps of cats over the age of eight (8) weeks to have them spayed or neutered.
(5) It is highly recommended that all trapped cats be tested for feline leukemia, and to have those who test positive humanely euthanized or isolated indoors.
(6) Identify all sterile cats by tipping their ears (tipping to be done by a licensed veterinarian); micro chipping is recommended but not required.
(7) Arrange to have all trapped cats spayed or neutered and vaccinated for rabies in addition to any other vaccination or immunization requirement imposed by the Commonwealth. It is recommended that such cats be vaccinated for distemper.
(8) Any animal known to have an infectious, untreated disease shall not be released back to the colony or any other outdoor environment where the disease can be spread to uninfected animals.
(b) It shall be the duty of the animal control officer or a deputy animal control officer to issue notice of non-compliance specifying that the caregiver has forty-eight (48) hours to provide a written response including how the colony will be brought into compliance within a ninety-day time period. The caregiver shall make weekly progress reports to the animal control officer.
(c) Failure to comply with any provision of this section shall constitute a violation of this section as well as section 5-38 and subject to penalties thereof.