An example of cause and effect is someone pressing a gas pedal, thus causing the car to accelerate. Getting an umbrella because it is raining is also a cause and effect example. Any pair of actions in which one causes the other is cause and effect.
There are infinite examples of cause and effect because it is a very broad topic. It can be used in many different contexts, including literature, marketing and scientific research. Cause and effect is simply the consequences of an action, and this can be negative or positive. The "what happened" consequence is the effect, while the "what made it happen" action is the cause. A negative example is that an effect of not paying bills results in the disconnection of a service.
Cause and effect can be small or large. Pushing on a pencil causing it to roll is a small example, while a large one is an earthquake in the ocean causing a tsunami. Neither the cause nor the effect has to be tangible, it can be intangible as well. An example of an intangible effect is a comment causing someone's feelings to be hurt. Studying a written work for cause and effect is a good way to practice critical thinking and reading comprehension.