Thanks to our association of them with filth, poverty, disease, and death, rats are almost universally loathed and feared. We blame them for the plague (also known as the "black death") that wiped out a third of Europe's population in the Middle Ages. We dislike the look of them, finding their long, pointed snouts, sharp teeth, beady eyes, and thick ropy tails visually unsettling. We're bothered by how they go about their business, finding fault with their lurking in the shadows of inhabited areas to feast upon garbage. And we're disturbed by how many of them might be living unnoticed in close proximity to us, fearing that they may have us outnumbered.
Folklore has long associated this class of rodent with calamity. Rats are believed to have a sixth sense regarding death and disaster; thus, by studying their actions, one can pick up timely warnings about misfortune headed one's way. As to why this might be so, it is said rats come by their foreknowledge about human events because they house the souls of the deceased.
Pay particular attention to the sight of rats deserting a ship, especially one still in port. Such an exodus is said to presage a disaster that will shortly befall the ship, even if the vessel is one that appears entirely sound.
In 1889, three people working on the Paris C. Brown, a riverboat that sailed between Louisiana and Ohio, spotted some rats leaving the ship. They decided to heed the implied warning and not reboard the vessel. Shortly thereafter, the Paris C. Brown struck a snag which went through her hull, sinking the ship in a matter of two or three minutes. While there were survivors of that wreck, the accident killed eleven.
On the other hand, rats seen boarding a new ship should be taken as a good sign.
It is also very unlucky to utter the word "rat" while on a ship, with such prohibitions having been noted as far back as 1886. One should therefore find a substitute word to use for such occasions.
Similar to the "rats leaving a ship" belief, the sight of rats abandoning a house for no apparent reason should be taken as a bad sign — either the structure itself is about to collapse or dire misfortune looms over one of the home's inhabitants.
Speaking of predictions of harm befalling particular individuals, rats gnawing on one's clothes or chewing on furniture, especially bedroom furniture, is an omen of death. Pliny even noted this in his A.D. 77 Natural History (albeit about mice rather than rats): "By gnawing the silver shields at Lanuvium, mice prognosticated the Marsian war; and the death of our general, Carbo, at Clusium, by gnawing the latchets with which he fastened his shoes."
Also similar to the "rats boarding a new ship" belief, an influx of rats into a structure supposedly indicates the homeowners will soon be moving, or possibly that they are about to come into money. (Rats apparently know where the good times are.)
As to how to get rid of rats, superstition holds that the most effective way to empty a home of them is to ask them to leave. One method is to sit by the rat hole and politely request that they move on. Another method is to write a letter to the vermin, preferably a short note that politely asks them to leave the property and recommends a nearby structure where they will likely flourish (such as the home of a disliked neighbor). Said missive should be neatly penned, folded, and shoved into the rat hole.
Writing notes to rats in supplication of getting them to leave is an old practice, one that dates as far back as the first century. This example comes from 1869:
Rats and mice,
Leave this poor person's house,
Go on away over to the mill
And there you'll all get your fill.
A sudden massive increase in the number of rats in a community is taken as a sign of imminent war, with that belief noted as far back as 1682.
Dreaming that one is being attacked by rats is said to reveal that someone in your waking life harbors plans to harm you.
Finally, because rats are thought to have extremely strong teeth, when a child's baby tooth is to be discarded, it should be done by leaving it near a rat hole along with an appeal to the rats to "send a stronger one" in its place.