I use Roundup or Crossbow. Nothing I know of will compete with thistle. Pulling them is futile; you can't get the root out that way, so you just slow them down. You can slow them down by shading them, but that won't kill them. Giant sunflowers will shade them in late summer. I am a strong advocate of returning as much land as possible to native conifers. They will eventually kill the blackberries and thistles, and will require no watering, as well as all of their other environmental positives.

Another thing that works is to cover an area of ground with black plastic in Spring when the plants start growing. In about 3-4 weeks, everything under the plastic will be dead. I use this method for killing grass when I want to put in a garden.

Can you cut the area with a lawnmower? Eventually the mowing will kill most thistles. As an alternative, I use Weedex rather than roundup -- it seems to kill them just fine and it leaves the grass. Mind you, I haven't got rid of them all either. Good luck.

Depends upon which thistles you have.

If the annual sorts, removing them will be the end of it unless, of course, the thing has already sent its seeds all over. In that case, you'll have the offspring next year. If so, deal with them when they're small.

But if you have colonies of thistles, most likely you have Canad thistle. That's a perennial and has persistent running root stock. A tougher thistle to get rid of but you can do it.

This page targets wholesale nurseries but you can easily extract info & photos which will be useful to you.
http://oregonstate.edu/dept/nursery-weeds/email_pubs/thistles/thistles.html

Here is a link that might be useful: Canada thistle

I killed thousands of them this last May and June with Crossbow, which does not kill grass if directions are followed. Most of them died after one application. I recommend that you buy the blue dye that you mix with the spray. It will help you figure out which ones you've already sprayed.

Thank you all for the suggestions. I'd prefer not to use an herbicide. That's why I'm asking if there's anything I could plant that would successfully compete with the thistles. Any other ideas?

You might want to think about what use you see for the land. Some great threads already exist along these lines, you can find them by searching "wildflowers". Here are a couple-

Wildflower meadow...How to maintain???
http://forums.gardenweb.com/forums/load/nwest/msg1015212522951.html

problems establishing new ecoturf lawn
http://forums.gardenweb.com/forums/load/nwest/msg052234187740.html

I have some very invasive plants that are stronger than thistles but you may never get rid of them either-
Vinca major in part shade purple flowers in spring
Symphytum grandiflorum, ground cover comfrey blue flowers in spring

If you'll indulge a query: Do you have to use newspaper under the mulch for the weed control? Wouldn't the mulch be enough to smother the plant material beneath it if it's applied thickly enough?

I used cardboard and mulch to bury thistles in my veggie garden this past summer and it worked. Check out the soil forum on G/W to find out more about the benefits of this type of gardening. It's been a fun experiment for me and the veggies grown are great.

We put cardboard down and wood chips on top of the cardboard around the immediate area of the raised beds in the kitchen garden. But the "wild" area I'm talking about here is huge, really huge. We couldn't even begin to cover it up in any practical way. That's why I'm interested in finding competing plants, if only to improve the looks of the area.
So the suggestions about wildflowers, sunflowers, and invasive ground covers are more what I was looking for.

So here's my dumb question: Do I widely broadcast the seeds (just toss them out everywhere and cross my fingers)? Or do I need actually to plant each seed in the soil and cover it up? And would I do that now, later in winter, or in early spring?

Thanks again for all the input!

To Estrya:

With pernicious weeds and other undesireables, the newspaper layer is good insurance. Mulching alone may or may not smother the nasties, whereas the newspaper, especially if you live somewhere typically PNW moist and mossy, forms a tight, paper mache-ish cover, immune (granted only for a time) even to the evil creeping bindweed.

To Toad ca:

Yes, a huge area would be too much for the smother method. Hemnancy gave you some great threads to check out. Just bear in mind that you cannot skip down your figurative garden path, blithly tossing handfuls of seed. Soil preparation and other good plantsmanship methods are still required.

Sounding like a downer,

Rain

Goats.

I don't think even goats would eat thistle!

And I wouldn't put much effort into groundcovers or annuals to outrun thistle either.

About the only thing I can think of that Might outcompete thistle would be ... scotch broom and himalayan blackberry.

Hate to rain on your parade, but thistle's are tough and there's no easy way to get rid of them without heavy duty chemical warfare. Pulling and tilling are worse than useless. Mowing doesn't faze them - btdt. Thistle grows just fine in even regularly-mowed lawns. Brush B Gon was what worked for me. Even multiple layers of cardboard with several inches of wood chips only worked somewhat - the Canada thistles have no problem running along underneath til they can work their way through a weak spot or out from under the edge.

Shading them out with native conifers is the only long-term solution - works on scotch broom and himalayan blackberry too. But while the conifers are growing in, you have to keep all three nasties whacked back with a brush blade or with herbicides so they don't smother the young trees and/or set seed.

You're not dealing with your average garden plant here. No, what you've got on your hands is a plant that's quite capable of world domination. You can't pull punches with it because it's determined to outcompete you, and only a few equally vicious plants stand a prayer of holding their own against it.

You can inject or paint an herbicide on the plants and that reduces the use of it a great deal. This is best done on a warm summer day, though.

I use a little handheld pump-up sprayer which is readily available for around $15. They are really nice to use, since you only have to pull the trigger to release a stream of spray. If you set the nozzle for a fairly narrow stream, you can carefully spot-spray each weed and use a minimum of spray. If you are dealing with thousands of weeds spread over a large area, injecting or painting each one will get very old, very fast.

If you buy the $5 squirt bottle type, you will regret it. They don't last, and they leak spray all over your hand.

Don't buy the ready-mixed weed killers at the retail stores. They are mostly very expensive water. You need Crossbow 50% concentrate or something like it, or you'll end up spending $1000 before you're through. If you make your Crossbow solution too strong, you will kill your grass as well as broadleaf weeds.

If you are worried about chemical exposure, get a pair of chemical-resistant rubber gloves, easily obtainable. If you don't pump up your sprayer to a high pressure, you should not get much mist blowing around. Low pressure makes big droplets that don't blow around much.

Next week is shaping up to be a good one for zapping weeds, weather-wise. You'll never find the perfect solution to this problem. I've been looking for one all my life, and I'm still using spray. The ecologically pure techniques are not applicable to large areas, sadly, unless you have an army of slaves.