I don't honestly quite understand the *desire* to get rid of them -- they are green, they have cute white flowers in the spring, and VERY tasty strawberries, and the leaves turn an attractive red come frost -- but, I suppose if you really WANTED them gone for some reason, the most sensible thing would be to rake and handweed. The runners "catch" very well, and the plants are not hard to pull up. You will have to keep after it for a while, but it is definitely a manageable problem.
In a more fundamental sense, they usually do best (in terms of competing with grasses etc) in low-nutrient acidic soil, so improving your soil with compost and checking the pH would help other plants outcompete them better.
I just leave them be, in most places. Am actively encouraging them as a groundcover in one large bed behind the house. I do pull them out of some other beds, just b/c I have other aesthetic plans for those beds, and find that hand-weeding easily keeps them in check with little labor.
I am in complete agreement with Pat....In fact, I was using them as ground cover under my Rose of Sharron. Last year, the plants were kind of tiny. This year, the leaves are as big as my regular strawberry plants. I think pulling them is no big deal, but you might want to keep a few....