Animal bites and scratches, even when they are minor, can become infected and spread bacteria to other parts of the body. Whether the bite is from a family pet or an animal in the wild, scratches and bites can carry disease. Cat scratches, for examples, even from a kitten can carry "cat scratch disease," a bacterial infection. Other animals can transmit rabies and tetanus. Bites that break the skin are even more likely to become infected.

I should say that for superficial bites from a familiar household pet who is immunised and in good health:
Wash the wound with soap and water under pressure from a tap for at least five minutes, but do not scrub, as this may bruise the tissue. Apply an antiseptic lotion or cream.
Watch for signs of infection at the site, such as increased redness or pain, swelling, drainage, or if the person develops a fever. Call your physician or health care provider right away if any of these symptoms occur.

Good advice, but for deeper bites or puncture wounds from any animal, or for any bite from a strange animal:
·If the bite or scratch is bleeding, apply pressure to it with a clean bandage or towel to stop the bleeding.
·Wash the wound with soap and water under pressure from a faucet for at least five minutes, but do not scrub, as this may bruise the tissue.
·Dry the wound and cover it with a sterile dressing, but do not use tape or butterfly bandages to close the wound, as this could trap harmful bacteria in the wound.
·Call your physician or healthcare professional for guidance in reporting the attack and to determine whether additional treatment, such as antibiotics, a tetanus booster, or rabies vaccination is needed. This is especially important for bites on the face, or for bites that cause deeper puncture wounds of the skin.
·If possible, locate the animal that inflicted the wound. Some animals need to be captured, confined, and observed for rabies. Do not try to capture the animal yourself; instead contact the nearest animal warden or animal control office in your area.
·If the animal cannot be found, or if the animal was a high-risk species (skunk or bat), or the animal attack was unprovoked, the victim may need a series of rabies shots.
·Call your physician or healthcare provider for any flu-like symptoms such as a fever, headache, malaise, decreased appetite, or swollen glands following an animal bite.

Of course the biggest fear with bites is if the animal has rabies. Luckily in the UK rabies is not present but in other parts of the world is a real concern.

Rabies is a viral infection of certain warm-blooded animals and is caused by a virus in the Rhabdoviridae family. It attacks the nervous system and, once symptoms develop, it is 100 percent fatal in animals, if left untreated.
In North America, rabies occurs primarily in skunks, raccoons, foxes, and bats. In some areas, these wild animals infect domestic cats, dogs, and livestock. In the United States, cats are more likely than dogs to be rabid.
Generally, rabies is rare in small rodents such as beavers, chipmunks, squirrels, rats, mice, or hamsters. Rabies is also rare in rabbits. In the mid-Atlantic states, where rabies is increasing in raccoons, woodchucks can also be rabid.

Yes by far the most important thing about bites and scratches is the threat of rabies. The rabies virus enters the body through a cut or scratch, or through mucous membranes (such as the lining of the mouth and eyes), and travels to the central nervous system. Once the infection is established in the brain, the virus travels down the nerves from the brain and multiplies in different organs.
The salivary glands and organs are most important in the spread of rabies from one animal to another. When an infected animal bites another animal, the rabies virus is transmitted through the infected animal's saliva. Scratches by claws of rabid animals are also dangerous because these animals lick their claws. The incubation in humans from the time of exposure to the onset of illness can range anywhere from five days to more than a year, although the average incubation period is about two months. The following are the most common symptoms of rabies. However, each individual may experience symptoms differently. Symptoms may include: