What is the name of a viney plant with small blue clustered flowers edged in white called?

Answer 1

'Heavenly blue' morning glory
Solanum or Nightshades flower in clusters. Later they have red berries.
Thunbergia grandiflora "Bengal Clock Vine", "Blue Sky Vine"
Vinca minor (Periwinkle) vining groundcover
Veronica repens This sprawling low grower might be called viney. It produces tiny true blue flowers.
Blue flowered clematis
Asarina scandens "Sky Blue" is a smaller and more delicate annual vine, with gloxinia-like trumpet shaped blooms.

Try Garden forum: Identify this plant
http://davesgarden.com/forums/t/705607/
http://www.gardenbuddies.com/forum/messages/4336/4336.html