Climbing plants are particularly useful in the garden because they allow you to increase productivity by using vertical space that would otherwise be empty. They are especially valuable in hotter climates, as they can be used to create the shade that is so essential for comfort. Their exuberance and appearance makes them one of my favorite groups of plants. See Where to plant for ways to use them in the garden.
Climbing plants grow rapidly once established, because they don’t waste a lot of energy creating a structural skeleton for themselves. This lack of structure means they need something to hold them up and they have developed various methods for holding on to their supports.
The twiners simply grow in a clockwise (or is it anti-clockwise?) direction and twine themselves up around anything that gets in their way (including each other). Hop, Kiwi, Akebia, Beans and Malabar Spinach all grow in this way.
The clingers (Ivy, Virginia Creeper) cling to walls or trees by means of roots or sticky tendrils. These species are the most effective plants for training directly on to walls, but I don’t know of any useful species in this category.
Tendril bearing plants grab on to small twigs with their tendrils. They include the Passion Vine, Peas and Cucurbits. These may also twine around their supports to some degree.
The sprawlers don’t actually climb, so much as grow through other vegetation. Some (Blackberry, Rose) use thorny stems, other have Velcro-like hooks to get traction. These species often need encouragement to go where you want them, in the form of tying in. They grow best on wide supports that aren’t very high.