"Common ivy" and "English ivy" are common names for Hedera helix. A popular groundcover due to its attractive leaves, this groundcover is, nonetheless, considered an invasive plant in parts of North America.
An important word in that last sentence is "parts." The Pacific Northwest is known to be one part of the country where common ivy is an invasive plant. But unlike Japanese knotweed or purple loosestrife (the prior entry), it may not be invasive everywhere. Consult local experts if you are unsure of the plant's status in your own region.
Besides spreading out of control on the ground, common ivy also climbs trees, as my picture shows. Although its popularity even landed it a place in the Christmas carol, "The Holly and the Ivy," it's best to avoid planting this over-zealous vine. Many homeowners, having discovered what an uncommonly difficult task it is to eradicate common ivy, hate this groundcover as much as they would any weed.