If planted without support, a tomato will sprawl all over the ground, which is how nature intended for tomatoes to grow. But for decades gardeners have preferred to stake or cage tomatoes. Tomatoes grown vertically take up less space, seem to develop fewer diseases because the leaves aren't in contact with the ground, and may be harvested while the gardener's standing up. Pole beans too like to grow upward. Bush beans seldom grow taller than a few feet, whereas pole beans will climb five or six times as tall.
Cucumbers are another example of a vegetable that likes to grow vertically.
But it's important to pick the right variety. A bush-type cucumber's vines won't grow more than a couple of feet out from the base of the plant. The more familiar vining cucumber is an aggressive climber, whether grown on a trellis, a fence, or a section of reinforced steel mesh stuck in an oak barrel. In the landscape the most familiar climbing plants are vines, which climb in various ways. And some vines simply wrap around whatever support is available.