These are just quickly written down, but I hope these can serve as sufficient answers.
Plant Behaviours:
1. - Some plants know when the sun will rise. Sunflowers are a good example of exhibiting this behavior called "Circadian Rhythm."
2. - Plants that have vines search for a surface, preferably a pole but walls are acceptable, to climb and grow on, which is called "Twining."
3. - Some plants 'curl up' whenever they are touched.
4. - Corn seeds can distinguish between 'up' and 'down,' which is called "Gravitropism."
5. - A plant can distinguish their own roots from another plant's.
Animal Behaviours:
1. - Animals can communicate, actually, they can communicate quite well! Dolphins and bees are infamous for this, as they communicate through a series of actions and the point comes across clear to others in their species.
2. - Body language is a behavior most commonly associated with animals, even though we do it too.
3. - Territorial/'Defensive' behaviors are common, such as marking and hostility when another animal trespasses into their domain.
4. - Certain behaviors are exhibited to attract/court mates, such as birds singing songs or chemicals being thrown off to lure in a partner.
5. - Cooperation is also a very common behavior, as seen in ants.
6. - Annual cycles, such as migration and hibernation.
7. - Animals also have a circadian rhythm like plants, which aids in whether or not an animal exhibits the behavior of being nocturnal.