The New York Times has a nice article on hospitals that allow patient's pets to visit. This is a controversial area, with policies (when they are actually present) that range from wide-open access to complete prohibition. Like most things in life, there's a middle ground that's the most reasonable.
The positive aspects of people being allowed to have their animals come visit are pretty obvious, since people may have close bonds with their own pets and having a chance to see their pets might make a big difference to their mental state/well-being, particularly for someone who is chronically ill.
The negative aspects are less clear. We certainly know that pathogens can be transmitted from animals to people (and in the other direction too), and people in hospitals are often at higher risk of infection and complications thereof. There's a list of pathogens we worry about, but there's a serious lack of data to help determine the severity of the risk - and how to reduce it. Organized pet therapy programs are great because they are structured and there can be a lot of scrutiny and training of the pet and handler. Visits by patients' own animals are inherently less controlled, since the individual animal and handler don't undergo the same degree of assessment and training.
I get asked to review visitation guidelines frequently, and a reasonable middle-ground can usually be found. These are some snippets from the NYT article that highlight common points.
A doctor’s order allowing the family pet to visit is typically necessary...
That's a good approach, although it's not often used. This lets the doctor decide if it is reasonably safe to have the pet visit, i.e. the patient is not at a very high risk of infection. The weak link here is sometimes the doctor, because sometimes the doctor doesn't understand the risks associated with pet contact and may not identify a concern. Other times, the doctor may not understand the relatively low risk and the potential benefits, and therefore default to banning visitation without giving it much thought. I think that's less common these days but still an issue.
...as is an attestation from a veterinarian that the animal is healthy and up to date on all its shots.
The first part is great: making sure there are no health or behavioural issues with the animal that would pose an increased risk. The second part is very common but largely represents a lack of understanding of the issues. Too often, "has he had his shots?" is the main question that's asked about the animal, despite the fact that it's largely irrelevant from a zoonotic disease standpoint. Yes, we want to make sure the pet's rabies vaccination is up-to-date, but the other core vaccines are irrelevant from a human health standpoint (although they're very important for keeping the animal healthy overall).
Most institutions require that dogs — the most common visitors, by far — be groomed within a day or so of a visit and on a leash when they walk through hospital corridors.
Standard and logical policy. Grooming might help reduce the burden of bacteria, fungi and parasites on the haircoat, as well as a lot of loose fur and dander that could otherwise contaminate the hospital environment.
Cats must be taken in and out of the institution in a carrier.
Logical. Some cats do well on leashes but it's better to have a cat in a carrier when taking it through a strange area. It also helps prevent other people from coming into contact with it.
If a dog or cat wants to get up on a patient’s bed, a covering is laid down first.
Good policy, and it protects both the patient and the animal.
If an animal seems agitated or distressed when it comes into the hospital, staff members who meet the family and escort them to the patient’s room have the right to turn it away.
This has two important components. One is that the visitation is supervised, which is great. The other is that staff are given the ability to intervene in the unlikely even that there are problems.
If the patient shares a room with someone, that person must agree before a pet may visit.
This is often overlooked. Roommates might be afraid or allergic, and in those situations, visitation shouldn't happen in a shared room. There might be a way to do the visit in another room, so it doesn't necessarily preclude the visit from happening. This has to be broached in advance and in a manner that the roommate doesn't feel pressured into consenting. It's best done by having the patient's healthcare providers approach the other patient and/or the other patient's family.
There's always some risk with animal hospital visitation. That's never going to be eliminated, but a lot of common sense practices can reduce the risk to a very low level, hopefully to the point that the risk is overwhelmed by the benefits. A little structure and a lot of common sense go a long way.