I have a small garden with herbs, lettuce and a couple of tomatoe plants. I have a vine like plants that has started growing there and is winding around all my plants. It has green leaves that look like small elephant ears. My husband describes the leaves as heart shaped. It winds tightly around the stocks of all my plants.
Sounds like Convolvulus sepium, bindweed. http://www.agf.gov.bc.ca/cropprot/weedguid/bindweed.htm or some other Convolvulus. This is a pest. It easily sprouts from seed and comes up from the roots. When you try to pull it off plants, you can end up causing a lot of physical damage. Try to pull as much out as possible and don't let the flowers go to seed.
even without a pic, i think eric has the id correct. this is very, very invasive and hard to get rid of!! when pulling it up, it's best to do so when the soil is moist and actually use a spade to dig down to get all the roots and then follow the feeder root along underground as far as you can. try to get it all up and all the little bitty pieces, too. this thing is one of the types that will grow underground for as far as they need to to get to light again...it's in the beds of the office building i work in...started in one small bed on the side and then showed up, the following year, in the bed out front and they are separated by 6 feet of blacktop... it takes persistance and diligence to get rid of this!! since it's in with your vegy's you're going to have to keep on top of it or it'll end up smothering the things you want to grow. good luck!!
Another weed, and vine, that is very similar to bindweed in wild buckwheat. Bindweed has showy flowers however, while wild buckwheat has smaller more inconspicuous flowers. Here's a pic of wild buckwheat. http://gardeningfromthegroundup.us/wild%20buckwheat.jpg
