If you're like me (let me offer my condolences), you look at those vines on plants and wonder, often aloud, "How in the world do that do that?"

This video answers that question.  Here's an explanation from the Sciencetrack blog:

This movie shows the extreme nutational movements of morning glory vines. Climbing vines need to find a suitable support on which to grow. Shortly after germinating, the young plant begins what appears to be a hunting motion in which the shoot tip rotates in a nutational movement. This swinging around of the tip is thought to help the plant bump into a support. If the shoot rubs against a support with the right shape, the rubbing induces a thigmotropic response (tropism induced by touch) and the shoot begins to curl around the support. This movie shows three morning glory plants at the stage where they have just begun "looking" for a support to climb. Vines typically show the most extreme nutational movements. The images were captured at 10 min intervals.

Nutational movements!  Of course!