Posted: 01/06/2013 at 13:53
Akebia and Hydrangea petiolaris (Climbing Hydrangea) come to mind as does most Clematis and even the Kiwi Vine.
Has the nieghbour said that you can grow things on their fence? If it is theirs then you have no right to touch it - so no staining, painting, hanging clothes lines, plants etc on it. Better to ask (on paper in case they move) before adding vines to it.