Even outside the academic arena, chemistry teaches us about our world.  So many people do not understand simple things such as why water is so heavy because they never learned about water's molecular structure.  The knowledge of the elements and other scientific basics also aids people in understanding medical explanations from their physicians as well as nutritional facts. And, as mentioned in post #3, the mental and mathematical exercises involved in a chemistry course have extensive benefits.

The study of chemistry forms a foundation for many other sciences.  If you take it in high school, it will be much easier in college.  You will be at some advantage because it will not be completely new.  Chemistry is needed for any science major, including medicine. 

Besides its usefulness, chemistry is just neat!  It is useful for cooking, crafts, and all kinds of other household areas.  All of us should also have an understanding of chemistry, because we will all need to take medicine!

The coolest thing I learned in high school chemistry was, pretty much everything I needed for college chemistry.  That may sound silly, but if you are planning on taking any type of career path that would involved chemistry classes in college you MUST take high school chemistry.  I took two years of chemistry in high school, and was amazed at how easy college chemistry was!  I made an easy A in a very hard class due to my background developed in high school.

Some students think  they don't need chemistry, but science classes are becoming more advantageous than ever before. Just because you might not be a chemist someday doesn't mean you won't learn something valuable from a chemistry class. For one  thing, with the way things are made and processed these days (including food), some basic knowledge of chemistry will help you understand what you are using, buying, and eating.

Environmental issues are only going to become more and more important. Many of these issues involve concepts that you are going to learn about in chemistry. In order for future voters to make informed decisions about anything that involves chemicals or chemical reactions (which is just about everything) you need to understand the basics.

There are some high school students who are going to take chemistry next year and be shocked with how much they love it. It will become the passion of their life. And they never would have known without the class.

By the way, I'm not a chemistry teacher!

Beyond what these other two posts have said, it is important to have a basic knowledge of some fundamental ideas just to be a well-rounded person.  For example, it is good to know the ideal gas law so that you understand the relationship between pressure and temperature.  That one helps me know that when I'm trying to boil water in a hurry I can press down on the lid and make the temperature rise.  Every educated person should know a bit about everything and that is something you can gain by taking Chemistry in high school.

There are two kinds of learning going on in high school chemistry classes.  The more obvious one is the empirical knowledge, the terms and actions of the science of chemistry, which always serve us well in everyday life even if we do not make science our career.  But the other form of knowledge, the cognitive processes, are absolutely invaluable.  The taxonomies of the elements, represented so powerfully in the visual arrangement of Mendeleev's Chart, teach us how to gather the units of any set into coherent, workable groups (for example, kinds of cars, kinds of animals, kinds of entertainments, kinds of information retrieval methods, etc.); the carefully designed chemical experiments teach us how the order of steps in a process is important for reliable, predictable results (for example, in building a structure, in baking a cake, in planning a trip, etc.) the way in which elements combine into molecules and the way that molecules combine into substances are indispensible skills in all disciplines; the exchanges of energy, in all their complexity, are learned and demonstrated, often in highly visual ways.   The ever-present dangers of chemicals teach us the importance of care and precaution, and the difference between seriousness and horseplay. In other words, the chemistry class is the training ground for logical thought, for organizing knowledge into useable patterns, for beginning the conscious use of our reasoning abilities for solving problems, a necessary passage from childhood to maturity.  And for many, it is the first stepping-stone to a life of scientific inquiry.