Answer: Based on your description I suspect the plant you have is the evergreen, vining English ivy (Hedera helix) rather than the low growing weed commonly called ground ivy. English ivy can smother other plants by blocking light and air and its weight can be detrimental to trees and shrubs. It would undoubtedly be a good idea to remove it from shrubs and small trees. (Larger trees can also be damaged by it if it creates a large mass within the canopy of the tree, thus working as a sail in heavy winds.) To remove it, pull the vines away and cut them off. Incidentally, the plant is very useful as a ground cover in many situations, especially in areas that are too shady or for some other reason unsuitable for lawn -- too steep, poor soil, tree root competition, and so on.
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