There are some stories about rainforest trees that can creep along the forest floor by growing new roots on one side and letting the roots on the other side die away, but these seem to be myths without much real scientific support. However, there are plenty of plants (strawberries are a good example) that can move, in a way, but sending out runners or shoots along the ground that then grow new roots and basically make a new plant in a nearby location. At first the 'daughter' plant is connected to the original plant, but if the original plant were to die, the daughter would remain. Since the two plants are genetically identical, this is sort of like the plant moving itself. And let's also not forget that almost all plants move all over the place at one point in their lives - when they are seeds!

If they float, yes, but ordinarily plants are rooted to the ground. The way that plants disperse is by sending propagules, spores and seeds, to other areas to colonize them. Thus, populations can move, but individuals can't.