Linked from
The 6 pages that link to Twining plant, each with the reason it gives.
TrellisRelated: Twining stems need upright members they can wrap around.
ConvolvulaceaeRelated: Twining stems are common in the family, though not universal.
IpomoeaRelated: Many Ipomoea vines climb by twining rather than attaching with tendrils.
WisteriaRelated: Wisteria climbs through stem twining rather than tendrils or adhesive pads.