So, what to do? Lock them in a part of the house with no carpets? Decide that they will be an outside pet from now on? Farm them off to some friend or relative who has no sense of smell?
Before we do anything drastic, take them to the vet to see if they have a medical problem. Here is a run down of some of the most common icky-producing problems I see every week.
Cats that urinate outside the litter box
I see at least one of these a week. The first thing we do is check their urine for infection. If they have a UTI we can clear it up with antibiotics. Some cats have disorder where the urine produced by their kidneys is irritating to the bladder or produces crystals that can turn into bladder stones. If that's the case putting them on special food can help. If we find glucose in the urine we then test for diabetes, which can be treated with another special food and daily insulin shots. Lastly, if the urine is especially dilute the cat may be in early kidney failure, which can be slowed down with a special diet and medication.
If the cat does not have a medical condition, we assume the inappropriate urination is behavioral. Cats are like teenagers - they act out. Putting the cat on anxiety medications or adding cat pheromones to their environment can help a lot. Often cats who did have a medical condition will develop a behavioral issue after the original problem is resolved.
Dogs that urinate in the house
This is the time of year for dogs to have UTIs also. With cooler temperatures they don't drink as much water, so things tend to concentrate in the bladder. This can lead to urinary tract infections and possible bladder stones. We do the same testing on dogs as we do with the cats. In addition, dogs are more likely than cats to have bladder stones. These stones can be picked up on ultrasound or x-rays of the abdomen. Some stones can be dissolved with special food, but others need to be removed surgically. Once a dog forms a stone, it is assumed they will form more. So they stay on their special food even once the stone is gone.
Cats that vomit
This is also a common complaint. Often it is a simple hairball problem. Even if you don't see hair in the vomit, I still recommend treating with CatLax or another hairball laxative for a few days to see if that resolves the problem. If that doesn't work, or if they're really ill, they will need blood work to look for medical problems. Many of the same issues that cause cats to urinate outside the box can also cause vomiting. Cats can also have irritable bowel, which often doesn't show up on blood work. This is sometimes related to food allergies and can be treated with special food and steroids. Occasionally GI parasites can cause vomiting. Bring a stool sample with you when you visit the vet so they can check and see if your cat needs to be dewormed.
Dogs that vomit
Often dogs will vomit just because they ate grass or some leaves. If this is the case, they will still have a normal appetite and feel fine. If a dog vomits once or twice but seems fine, try withholding food and water for 12-24 hours to let the stomach calm down and see if that stops the vomiting. If a dog acts like it feels bad or vomits often, they need to be seen by a vet. Blood work can look for medical causes, fecal exam can reveal parasite causes, and physical exam may find abdominal pain that could mean a foreign body obstruction. Dogs like to eat non-food items like toys, sticks, clothing, or towels, and these can become stuck as they pass through the GI system. They usually will need to be removed surgically. Also, if dogs eat people food or other food that they're not used to (cat food, dead squirrels, etc), this can upset their stomach and lead to pancreatitis. This would need to be treated with medication and fluids, and often requires hospitalization.
I had a roommate in vet school whose cat liked to poop in my bathtub. Stepping on wet poop with bare feet at 6am is not peaceful. Poop is gross, and should only be found outside or in litter boxes. Both dogs and cats will sometimes poop in the house if they have parasites, so a fecal should be checked first thing. Also, some medical conditions like irritable bowel or food allergies can cause loose stools, and sometimes the animal just can't make it to where they're supposed to go in time. Lastly, pooping can be a behavioral problem just like urinating. If medical conditions are ruled out than dealing with behavior issues may be necessary.
Veterinary Partner is a website I often send owners to for information. They have good information on cat urinary behaviors, long term care of chronic conditions, and the basics on parasite control. Your vet is the best source of information for your particular animal, so don't be afraid to call them if you have questions!