What are some things in nature that have the Fibonacci sequence?

Obvious occurrences are in the number of "observable" spirals in the seeds of a sunflower, or on the outside of a pineApple, and in the number of leaves and petals on plants, for example clovers usually come with 3 leaves, daisies usually come with 55 petals. (3 & 55 are both Fibonacci numbers.)

As the Fibonacci numbers increase, the ratio between them gets closer and closer to the "Golden Ratio" φ which is approx 1.618034 (exactly it is (1 + √5)/2). Each petal or leaf of a plant grows from primordia and if the reflex angle between successive primordia is measured it is approx 222.5°; the ratio of this to a full turn is 360/222.5 ≈ 1.618 - the Golden Ratio. In using this spacing it provides the densest packing (for example with the seeds in a sunflower) making it stronger than radial spokes; it also means that each successive primordium gets placed in the largest space available.