In terms of behaviour, animals have plants beat – though some would argue that plants have their own brand of intelligence.
Not all photosynthesizing beasts are firmly planted, though, and many that live in the water can move. Aquatic algae, for instance, often have whip-like structures (called cilia and flagella) that they can use to propel themselves along in the water. Some land plants also produce flagellated sperm that can move on their own volition.
A single-celled marine algae with flagella for getting around. From Wikimedia.
In the ocean, the ability to move can be beneficial, allowing algal cells to find food or move to a suitable environment. Motile cells can also avoid their predators by swimming away – something land plants definitely cannot do. Swimming algae incredibly slow, topping out at about half a centimetre per minute – but a new study suggests that the slow race between algae and their predators might be responsible for a far bigger, more dangerous phenomenon.