PlantsVines
There is no taxonomic rank for vines. Here are some of the more common perennial vines.

Leaf Arrangement Leaf Complexity Tendrils

The following genera are arranged alphabetically by family.
Poison-ivy
Poison Ivy — Genus Toxicodendron
Family Anacardiaceae.
Bluevine
Swallow-wort — Genus Cynanchum
Vines. Leaves opposite, simple. Family Apocynaceae.
Two-flower Milkvine
Milkvine — Genus Matelea
Family Apocynaceae.
Climbing Hempweed
Hempvine — Genus Mikania
Family Asteraceae.
Common Trumpet-creeper
Common Trumpet-creeper —  Campsis radicans
Leaves opposite, pinnately compound, toothed. Flowering Jun-Aug. Family Bignoniaceae.
Coral Honeysuckle
Honeysuckle — Genus Lonicera
Shrub or vine. Leaves opposite, simple. Fruit is a drupe or berry. Family Caprifoliaceae.
Texas Bindweed
Morning-glories & relatives — Family Convolvulaceae
Vines. Leaves alternate. Leaf margins entire. Flower petals united, sepals separate. Cuscuta is a leafless parasite. This family now includes Cuscutaceae.
Cantelope
Squash & Melons — Family Cucurbitaceae
Vines with tendrils. Leaves alternate, simple, palmately veined.
Texas Bluebonnet
Papilionoidae — Subfamily Papilionoidae
Leaves alternate, once-pinnately compound or palmately compound. Flowers bilaterally symmetrical. 3 separate petals and 2 fused petals. Family Fabaceae.
Carolina Snailseed
Moonseed Family — Family Menispermaceae
Maypop Passionflower
Passionflower — Genus Passiflora
Vine with tendrils. Leaves alternate, simple, lobed. Flowers with 5 petals, 5 sepals, many threads. Family Passifloraceae.
No image available.
Queen's-wreath —  Antigonon leptopus
Vine with tendrils. Margins entire. Flowers pink or white. Flowering summer-fall. Family Polygonaceae.
Jumpseed
Knotweeds & Smartweeds — Genus Polygonum
Herb or twining vine. Stem nodes often enlarged. Leaves alternate, simple, with a sheath around the base of each leaf petiole. Family Polygonaceae.
Leather-flower
Leather Flower — Genus Clematis
Vine. Leaves opposite, pinnately compound. Sepals 4(-6), petal like, petals absent. Family Ranunculaceae.
Supplejack
Supplejack —  Berchemia scandens
Leaves alternate, simple. Flowers with 5 stamens. Flowering Apr-May. Fruit blue-black drupe. Family Rhamnaceae.
Common Balloonvine
Balloonvine — Genus Cardiospermum
Leaves alternate, compound. Family Sapindaceae.
Catbrier
Greenbrier — Genus Smilax
Vine. Leaves alternate, simple. 3 petals, 3 sepals. Fruit a dark berry with 1-3 seeds. Family Smilacaceae.
Peppervine
Peppervine —  Ampelopsis arborea
Vine with tendrils. Leaves alternate, compound. Flowers opposite leaves. Family Vitaceae.
Heart-leaf Ampelopsis
Heart-leaf Ampelopsis —  Ampelopsis cordata
Vine with tendrils. Leaves alternate, simple. Flowers opposite leaves. Family Vitaceae.
Virginia-creeper
Creeper — Genus Parthenocissus
Vine with tendrils. Leaves alternate, palmately compound. Flowers opposite the leaves. Fruit is a berry with 1 to 4 seeds. Family Vitaceae.
Summer Grape
Grape — Genus Vitis
Vine with tendrils. Leaves alternate, simple. Flowers opposite the leaves. Fruit is a berry with 1 to 4 seeds. Family Vitaceae.