Sharon Astyk (author of the blog Casaubon's Book) wrote a really neat article on weeds in her garden a while back. You will find it over at Hen and Harvest, dated October 12th. She mentions not mulching a portion of her garden just to see how it would turn out with the weeds providing competition for her plants. She weeded desultorily, that is, weeded a bit, but no great effort in keeping the garden weedless. This is more or less how I garden as well. I mulch, I weed, but I'm not a fanatic. Some weeds, if they are not harming the plants or overall yield of the produce, are fine by me. Some, indeed, are welcome and sought after and greeted with cries of delight when they're found (purslane and lambsquarter).
At any rate, it's a good article. Check it out.