What do I mean by twisty curvy plants? These are plants that have contorted and twisted stems. Commonly used plants like this include contorted hazelnut and corkscrew willow.
The contorted hazelnut (Corylus avellana 'Contorta') also goes by the name Harry Lauder's walkingstick. It is curiously twisted on a grafted stem. This plant grows eight to ten feet tall, but grows very slowly and can be pruned to keep it within limits. The habit is quite rounded to show the extremely contorted and twisted stems. Although a cultivar of the hazelnut commonly used for nut production, the contorted variety rarely produces nuts. Mine sends up lots of suckers, which have to be pruned back each year.
The corkscrew willow (Salix matsudana 'Tortuosa') is popular in arts and crafts. This unusual specialty plant is a small to medium-sized oval tree with interesting contorted or "corkscrew" appearance in its branching and leaves. The overall habit is oval, with narrow branch angles and contorted small branches. It grows 20-40' high and has medium green colored leaves with medium-fine texture.
Weeping plants are different from contorted ones, yet also are unique enough to need a special place in the landscape. There are many different weeping plants on the market.
The most commonly found are Weeping Willows (Salix alba), Weeping Cherries (Prunus subhirtella var. pendula) and Weeping Mulberries (Morus alba 'Pendula'). Consider a Weeping Dogwood (Cornus florida 'Pendula') or a Weeping European beech (Fagus sylvatica 'Pendula').
For something really different look for weeping evergreens. Each plant is so unique that it is hard to pick a favorite. I particularly like the Weeping European larch (Larix decidua 'Pendula'). There are also weeping white pine, weeping Colorado blue spruce, and weeping eastern arborvitae.
Consider a twisty curvy or weeping plant for your garden, but remember that they are very special plants. Their unique features require special consideration. Failure to take these into account can lead to disappointment. A weeping tree can become a major asset in the garden or a plant that looks oddly out of place.