People who are allergic to animals react to saliva, skin flakes (dander), urine or feathers. Avoiding the animal(s) causing the problem is the simplest solution, but isn't always possible. If your work requires being around animals, or if an animal is a beloved family member, there are some actions you can take to minimize the symptoms you develop around them.
Dogs and Cats
The most important step is making at least one area of your home where you spend significant amounts of time into an animal-free zone. The bedroom is usually the best choice for this. This permits you to get your needed rest undisturbed by a stuffy nose, wheezing, etc.
A poor second choice, if you simply can't keep your cat, dog, etc out of your bedroom is to hide your pillow someplace during the day (high closet shelf?) so the animal can't sleep on the pillow, shedding dander.
Adding a HEPA room filter will minimize the amount of allergen reaching your nose and eyes.
Brush your pet daily (outdoors, preferably by someone other than the allergic person) and wash the pet at least once a week.
There are no hypoallergenic dogs or cats. Dog breeds that shed less (standard poodle, airedale terrier, etc) are sometimes less bothersome to allergic people.
Horses and Cattle
You'd tend to think that only farmers, ranchers and riders would have to worry about these allergies- but horse and cattle allergens can be found in surprising places. Cosmetic and other brushes are often made from horse hair. These allergens can also be found in furniture stuffing, ropes, mattresses and rub pads.
Rats, Mice, Guinea Pigs and Hamsters
In addition to being problems for pet-owners, rat and mouse allergy can be significant among lab workers and researchers. Such allergies can occur in up to 30-40% of people regularly working with laboratory animals.
For many of these animals, immunotherapy is available, and can be part of a permanent solution to the problem.