From the most recent newsletter at www.carrollgardens.com:

Question: A bright yellow thread-like something has attacked several plants in my garden and appears to have killed them by covering and twining around the stems.

Answer: You have Dodder, a leafless, parasitic, morning glory relative. Dodder is an annual; new plants germinate from seed each spring. If they germinate near a host plant, they will attach themselves to it and extract the carbohydrates from the host. Dodder will bloom with little white blooms and drop seeds for next year's crop. It will sometimes kill the host plant totally.

Every thread of Dodder should be pulled off of the host plant and removed as soon as discovered, preferably before it sets seeds. Once fallen, ripe seed can remain viable in the soil for many years, so it is important to check broadly for several years in areas where Dodder has attacked plants previously. Two inches of shredded hardwood mulch spread upon fallen Dodder seeds will prevent them from germinating.

I've heard that, as a parasite, dodder enters the host plant, and can regrow from points of contact. So, it is not sufficient to remove the dodder itself; one is better advised to prune away the parts attacked by dodder and leave the healthy parts of the plant to grow back.

I've heard the best way is to spray it with a high nitrogen fertilizer. Forget where I heard that, probably on one of the Garden Talk shows I listen to.