What is the difference between deontology and consequentialism? What are some of the best examples of each theory?
Broadly speaking, consequentialism judges an action according to the consequences of the action. While a deontological judgement asks whether the action follows a given rule.
1) A main proponent of a deontological rule is Immanuel Kant. His fundamental rule is the categorical imperative. It states:
Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.
2) A main proponent of a consequentialist ethics is Jeremy Bentham. His prinicple of utilitarian ethics states:
By the principle of utility is meant that principle which approves or disapproves of every action whatsoever according to the tendency it appears to have to augment or diminish the happiness of the party whose interest is in question: or, what is the same thing in other words to promote or to oppose that happiness.
TLDR; they are about the right of everyone to define what is the best method to achieve the purpose.
In fact they are not as different as many people think:
Every rule have been estabilished to be so in either of following reasons:
On a whim of ethics creators.
Ethics creators followed some purpose.
In case of 1 we do not have any reason to accept such ethics as we also could use the argument "I want another ethics".
In case of 2 we must analyze what purpose is. Many people agree that purpose stands for some [set of] (desirable) outcome[s]. Thus, good enough consequences.
In this case only the one[s] who established the rules is/are allowed to define the purpose and best methods (at least the rules, but deontology does not reject other ethics) to achieve that purpose. And everyone must follow these established rules. This is the cornerstone of deontology.
On the contrary, consequentialism is about the right of everyone to decide what the best method to achieve the purpose is. Although, still not about the right to define the purpose itself.
P. S. About examples I agree with Jo Wehler.