I am in the fortunate position of having a neighbor with a hunting cat. I saw her catch a good sized rat the other day and carry it off into the woods from whence it came. I stood and applauded. That cat has cleaned out voles and moles for us too. Would love to give her a Christmas Gift Card!
Seriously, the right cat might be the answer.

Kania traps?

I have had rat problems years ago. At first I was suspecting rabbits. Then I made a rabbit trap. Then Got a rat. The same trap worked just fine on rats. I got maybe close to 20 of them. At the same time I was using other rat traps(similar to mouse traps). And at the same time I was feeding them rat baits, store bought and home made. I could not find out how many died of eating the baits. It took two seasons an I almost got rid of them.
Another way I discovered way drawning them. Fill a small bucket with water, about 6" empty. Make a sort ramp with a piece wood so they can go up, looking for water. They would check in but could not check out.

But my biggest problem was in the spring . They would eat tender seedlings.

Our local Humane Society will let you bring in feral cats, get them spayed/neutered and vaccinated for free, then return them to you for barn cats. They will also let you adopt fixed feral cats as barn/garden cats. I like this much better than poison which unfortunately killed a neighbor's mouser.
We now have about 5 or 6 mousers between the neighbors and us. We are on acreage, though. Nancy

I saw her catch a good sized rat the other day and carry it off into the woods from whence it came. I stood and applauded.

I praise my cat when she catches a vole, chipmunk, mouse, or other small rodent, and when she kills them quickly, telling her she's a "good hunter girl". However, she is only 6 pounds & change and a rat is probably out of her league. She tries to chase the gray squirrels, but they're out of her league too.

One of those little terrier dogs would probably be good, or how about something like a "rat zapper"?

Here is a link that might be useful: Rat zapper

Unfortunately I have a big dog that hates cats. She did catch a rat and kill it one day, but that was only when I had discovered the rat in some bushes, and chased it out, and she was there to pounce on it. But my garden area is fenced in from her, so any rats that go in there at night are safe from her.

terrene, have you actually used the Rat Zapper?
I've been wanting to get some chickens, but have hesitated cause the rats are drawn to the seed. We had rats really bad when we had chickens before! Of course with all those barn cats it might work after all! LOL Nancy

ccabal, if the dog cannot get into the fenced garden, maybe a cat would be safe in there? I have not known my lovely neighborhood cat to damage any plants.....

Plant some catnip, and the joint will become a real cathouse. Until the catnip ends at least. But I think Kania traps do a better job, and they don't start wild fights at 4am.

A few years ago I had a rat problem and I cured it with a live trap. I had a bird avary in my garden and the rats found a way into it and ate several birds. I caught 7 very large rats and of course I had to sacrifice them by drowning in a tub of water while in the cage. Evil little critters! I found that the same trap helps me to control the squirrel population to keep it low enough so that the squirrels (commonly referred to as tree rats) get only their fair share of my vegetables and fruits. You can get live traps from your local feed store. I use peanut putter as the bait in the live trap for both of these pests. Don't worry; you are smater than the rats! Although my wife says that the squirrels make me look kind of dumb.

Nancyjane, no I haven't. It was recommended on another website. No rats here though.

We have a small Hav-a-hart trap that works good for rats or squirrels. Peanut butter makes a great bait.

OK. The only way to deal with this problem is to eradicate the rats.
@ OP: If you are against using bait/poison, How about a LIVE rat trap (aka have a heart). Like the one shown in the picture below. Years ago I got the instruction from internet and make one myself. But if money is not the object you can buy them at the nurseries.

RAT MOTEL; THEY CAN CHECK IN BUT CANNOT CHECK OUT.loll

I've been seeking to get some poultry, but have hesitated cause the mice are attracted to the seeds they can be dealt with it.

TermiteRescue

This post was edited by ZaraMorant on Wed, Oct 30, 13 at 9:20

By a snap trap and put peanut butter on the tip of the trap and wait for the vermin to die. If that doesn't solve your problem call a professional like epmpestcontrol

Get one of these.

Seriously, if you live where there are bullsnakes, ratsnakes (notice the name?) or other rodent eating snakes, encouraging them to stay on your property will diminish the number of rats.

They might not eat many of them, but the surviving rats will flee to your neighbors.