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People and many animals have a skeletal system which gives them shape and holds them up. Plants have a fibrous system that gives them shape. Animals have a respiratory system to take in oxygen and remove carbon dioxide. Plants have a respiratory system that takes in CO2 and gives off O2. Animals have a circulatory system that moves essential fluids like water and blood. Plants can take in nutrients and move them through a living fiber layer to feed and water the plant. Both animals and plants need sunlight. Animals make some vitamins from sunlight. Plants use it for photosynthesis and food production. Both animals and plants have systems to get rid of unwanted waste products. 
It is kind of neat that a plant waste product, oxygen, is necessary for most animal life :)
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