Forested areas of the United States contain a number of native vines tall enough to climb into trees. Using this natural scaffold, they make their way from the forest floor into areas with more sun. While this is beneficial for the vine, it might not be beneficial for the tree. Some vines grow so aggressively they can literally smother a tree, eventually killing it. Vines with more restrained growth probably won't harm the tree unless you allow them to grow into the canopy and cover the leaves.
Wild Versus Native
Some invasive, non-native vines have escaped cultivation to become established in wild areas. An example is kudzu (Pueraria lobata), hardy in U.S. Department of Agriculture plant hardiness zones 5 through 10 and growing wild all through the Southeast. Other wild invasives are English ivy (Hedera helix), growing in USDA zones 5 through 9, and Japanese honeysuckle (Lonicera japonica), hardy in zones 4 through 10. These plants shouldn't grow in trees and should be removed if present. Native vines are wild, but they belong here. Most native vines don't threaten trees, but some will.
Aggressive Native Vines
Two fast-growing natives that can take over a tree are fox grape (Vitis labrusca) and trumpet creeper (Campsis radicans). Recognize fox grapes by the bluish-purple clusters of grape in fall. Hardy in USDA zones 3 through 7, vines can climb to 40 feet. Trumpet creeper has showy orange-red flowers that attract hummingbirds, but grow this vine on an arbor instead of on a tree. Vines grow to 40 feet long in USDA zones 4 through 9. Carolina jessamine (Gelsemium sempervirens) is a problem because it's evergreen, and can shade out tree leaves if it grows into the upper branches. Identify it by the fragrant, trumpet-shaped yellow flowers in spring. It grows in USDA zones 6 through 9. These three plants can be invasive.
Vines with Restrained Growth
Slower-growing natives that don't harm trees still need maintenance. Cut back the vines before they reach the tree branches. Check beneath the vines to make sure there are no cankers or wounds on the tree trunk. One possibility is passionflower (Passiflora incarnata). Vines grow perennial roots each spring and produce intricate lavender flowers. Hardy in USDA zones 5 through 9, the plants provide larval food for the Gulf fritillary butterfly. Another candidate is crossvine (Bignonia capreolata). The orange and red trumpet-shaped flowers lure in hummingbirds in USDA zones 5 through 9. Red tubular coral honeysuckle flowers (Lonicera sempervirens) also attract hummingbirds, and the red fall berries attract songbirds. The evergreen vine grows in USDA zones 4 through 10.
Remove an unwanted vine from a tree gradually. First, remove at least a 2- to 3-inch piece of vine near the vine's base. Rather than pulling the top of the vine from the tree, let the vine wither and die, and then take it down. You may have to repeatedly cut back new growth as it appears from the vine's base. If the vine has roots that store food, this could take a while. If the vines have moved into the upper branches, consider consulting an arborist for removal.