Certain plants always grow as vines, while a few grow as vines only part of the time. For instance, poison ivy and some kinds of bittersweet can grow as low shrubs when support is not available, but will become vines when support is available.
A vine is a growth form based on long, flexible stems. This has two purposes. A vine may use rock exposures, other plants, or other supports for growth rather than investing energy in a lot of supportive tissue, enabling the plant to reach sunlight with a minimum investment of energy. This has been a highly-successful growth form for plants such as kudzu and Japanese honeysuckle, both of which are invasive exotics.
The vine growth form may also enable plants to colonize large areas quickly, even without climbing high. This is the case with periwinkle and ground ivy.
Most vines are flowering plants. These may be divided into woody vines, such as wisteria, kiwi, and Common ivy, and nonwoody vines, such as ground ivy. Generally, climbers are always woody vines, while nonwoody or herbaceous vines are not climbers but rather groundcovers.
One particular group of plants has a growth form that's intermediate between shrubs and vines. This is the rose family, including roses, blackberries, and raspberries, all of which grow with semi-vining canes.
One odd group of vining plants is the fern genus Lygodium, called climbing ferns. Here, the plant's stem does not climb, but rather the fronds (leaves) do. The fronds unroll from the tip, and theoretically never stop growing. In the meantime, they can form thickets as they unroll over other plants, rockfaces, and fences.
Many of the clubmosses are also groundcover vines.