Answer:
Pure competition: This is a market that has a big amount of buyers and sellers. This is good for the consumer, because competition will cause prices to go down. Individual firms try to get their prices low enough that consumers choose them.
Monopolies: There is no potential for competition in a monopoly, because only one business or company determines prices, with no room for cross-competition. There are no examples of this because it's technically against the law, though historically in the Gilded Age people like Rockefeller and Carnegie had serious monopolies in serious industries.
Oligopolies: Oligopoly, meaning "rule of a few," is a system in which a couple of powerful companies control everything. If competition is eliminated and they cooperate with each other, consumers can be in trouble. The car market in the US is an example.
Monopolistic competition: This is when there is technically no monopoly, but the products are distinct enough that they're not substitutes. A company like Apple has something close to a monopoly because people are so devoted to their products that they can jack prices up.