Some of these movements are in a time scale much slower than what humans are used to call a movement. These movements are acutely guided by environmental cues, and are essential plant "behaviors" for them to survive in the challenging ecosystems.
Check out a nice slow time-lapse video showing how plants "dance" to the changing directions of the light.
Another cool video showing the slow motion of a germinating green bean. After a seed lands in a new piece of turf, it takes the right combination of environmental factors, light, temperature, humidity, etc., to trigger its germination. It is quite amazing how much force it takes for the young germinating seedlings to crack open the seed coat, and how the developmental program is intricately regulated to properly send shoots towards the light and roots towards the soil.
For example, plant flowers contain the right combination of color, scent, and taste to attract pollinators to carry pollen containing male gametes to the female gametes of a different flower.
Dandelions are hugely successful colonizing around the globe. This is largely due to the fluffy structure developed at each individual seeds, so that they can be easily carried to distance by wind.
You might be very familiar with Cockleburs (Xanthium), which take advantage of the moving animals in their surroundings to carry seeds to miles away from their parents.
Some peculiar plant species also evolved rapid movement. This is quite amazing, considering plants neither have muscles nor neural circuits that control them. What are the mechanistic basis for rapid plant movement?
The most famous case of rapid plant movement is probably in Venus flytrap (Dionaea muscipula), which can close their leaves in 100 ms triggered by touch of the trigger hairs.
Charles Darwin's illustration of the Venus flytrap, and he describes the plant as "one of the most wonderful in the world".
See a Venus flytrap in action. Besides the movement, the metabolic systems that go into making the sweet lure secreted on the surface of the catching leaves as well digesting the proteins from the preys are also quite remarkable.