A rat is any one of about 56 different species of small, nearly omnivorous rodents belonging to the genus Rattus. The most well-known rat species are the Black Rat and the Brown Rat. The group is generally known as the old world rats or true rats, and originated in Asia. Rats are bigger than most of their relatives, the Old World mice, but seldom weigh over 500 grams in the wild.
In Western countries, many people keep domesticated rats as pets. These are of the species Rattus norvegicus, which originated in the grasslands of China and spread to Europe and eventually, in 1775, to the New World. Pet rats are Brown Rats descended from those bred for research, and may be called "fancy rats." But they are still the same species as the common city "sewer" rat. Domesticated rats tend to be both more docile than their wild ancestors and more disease prone, presumably due to inbreeding. Rats have a significant impact on food production. Estimates vary, but it is likely that anything between 1/5 and 1/3 of the world's total food output is eaten, spoiled or destroyed by rats and other rodents.
While modern wild rats can carry Leptospirosis and some other "zoonotic" conditions (those which can be transferred across species, to humans, for example), these conditions are in fact rarely found. Wild rats living in good environments are typically healthy and robust animals. Wild rats living in cities may suffer themselves from poor diet and internal parasites but do not largely spread disease to humans.
The rat makes a fine pet, known for its intelligence, playfulness and sociality. They are extremely clean. Rats can be taught entertaining tricks, as many other domesticated animals. As with any pet, it is best to seek a rat from a professional breeder rather than a pet store.