Logical fallacies are pseudological arguments. They are statements that feel persuasive and truthy but if you pay close attention, you will see that they are not logically valid. Once you learn to recognize them, you will see that logical fallacies are everywhere: politicians use them in speeches, journalists use them in the media, advertisers use them and you will even find them in your own thinking.
It is important to learn about logical fallacies so that you can be a better consumer of facts, ideas and the media. You can quickly recognize who is speaking honestly, who is thinking critically, and who is not. Most importantly, this is a skill that will help you to sharpen your own thinking and analytical skills.
There are thousands of known logical fallacies. This page lists the ones that are included in the game of Sophistry. It has links to their definitions and famous examples.
For an even bigger list of fallacies, check out these resources:
List of Fallacies