While hospitals in the real world are usually places where people find care, in games they are often a reflection of our anxieties about what a hospital represents: a loss of control, disease, dying, and sterile environments.
Hospitals in the real world often do much to combat the popular apprehension about these places of healing, but popular media, including video games, are just as likely to exploit user fears.
This is not to say that all hospitals are safe, or that they don't sometimes contain unethical practices, but the ideal that hospitals, their staff, and their patients try to meet are often at odds with these uncomfortable exceptions.
Games which take a more detached approach to hospital care include Theme Hospital, where the player attempts to build a viable hospital business, while one famous example, Silent Hill, portrays a hospital as a source of horror.
As medicine continues to diversify and improve, and as hospitals actively combat their negative image, there may some day be a marked decrease in the public's negative perception of hospitals. But there may always be negative connotations, so long as humanity is susceptible to illness and injury.