Small dogs like rat terriers can do em in. The dogs do sometimes have the unfortunate habit of chewing and clawing at furniture, doors and walls to get at their prey. Cats are the best because they have the instincts and patience that is needed to be still and wait for the right time.
We have lived and again live at the edges of wooded areas in a city residential area. Rats and mice as well as racoons have a tendency to come in when winter approaches. One good cat can keep the vermin at bay. Haven't had a problem in years.
In my town in Indiana someone killed a cat that was living around some grain silo. The people where understandably very upset because the cat was put out there as a mouser and protected the grain from mice and rats. It made me angry because it was just such plain mean thing to do.
I grew up in a very upscale neighborhood, right on Long Island Sound.
The rats that I observed near the seawall were truly awe-inspiring (if that sort of thing inspires you). They were at least as large as my VERY large cat, but good old Mittens did 'em in anyway.
We should have had a rat problem but thanks to the cat (who was born in the wild, BTW) we never did. Mittens had a litter once, and taught all her kittens to hunt. They all grew up to be excellent ratters, and in fact, I now own one of her decendents, who keeps our house free of vermin.
PS: If it interests anyone, I have found that the female cats are particularly good at this job. I'd be interested to hear if anyone else has made this same observation, as well as hearing any theories as to why this might be.