While plants don't consciously communicate with each other they can receive certain cues from the environment around them and because of this a plant in effect can change the way other plants around it end up growing. These responses to the environment are called tropisms and there are a quite a few different types.
Plants will tend to grow towards the light (Phototropism), a vine will wrap around a tree instead of trying to grow straight through it (Thigmotropism), a branch will grow in a different direction when it comes into contact with a solid surface (again Thigmotropism), certain plants produce chemicals in their leaves which prevent other seeds from growing around it (Chemotropism), roots grow downwards shoots grow upwards (Gravitropism). There are many more examples too.
The presence of environmental stimuli alters the levels of plant hormones (particularly auxin) in different cells which causes the plant to grow in a different way than if the stimuli were not present. It's all automated and there is no thinking involved on the plant's part.