Plants move. Sunflowers turn through the day to face the sun. Carnivorous plants such as the venus flytrap can capture prey. A plant in the shade will grow taller in order to reach sunlight (over several days or weeks of course). Roots grow deeper to reach water.
Movement is not considered to be a necessity. While it is possible that an organism must be able to move in order to live (I can't think of any living organisms that live, but do not move) having movement as a requirement for life serves no purpose. This is because too many things move without being alive. Diffusion causes particles to spread. Crystals and stalactites grow in different directions depending on water/nutrition available. Water moves in currents. Even glaciers move. While movement may be required for life, the ability to move serves absolutely no benefit in classifying living organisms .
For example, we could say that all living things are made of matter. A requirement for life is that it must be made of matter. This is true, it is a fact. By this rule, expressions of energy (light, heat, sound, etc.) and empty space are not alive, as they are not composed of matter (we're ignoring quantum for the sake of the example). However, that would be all that it would eliminate. It would not eliminate rocks, water, chemicals, metals, and many more nonliving entities.
There are four requirements to be considered a living organism.
1) Ability to reproduce
2) Ability to respond to stimuli (this could be argued as ability to move)
3)Ability to grow
4)Uptake of nutrients, and excretion of waste
There are many more things which are required to live, and shared by all organisms. An organized structure. A membrane or some method of separating the organism from the environment. Every individual is a product of a former generation. But these classifications are not as simple as the basic requirements for living, and thus, do not serve any purpose in classifying living organisms (at least, for something as simple as whether or not it is alive).
Since its been thrown around a couple times, I'll also say that its still highly debated whether or not viruses are alive. And its entirely possible that once there is a definitive answer, the requirements for life may be changed. This is because viruses lack the ability to reproduce on their own; they have to hijack a living cell or bacteria, and use the cell's machinery for their own reproduction. And scientists argue whether or not this counts as a valid form of reproduction.