The Iodine Clock Reaction is classic chemistry in action. And it is amazingly simple. You can by a kit from a number of different science websites...or you can just go to your local grocery store to pick up basic supplies. You can use simple chemicals that you can find nearly anywhere, like vitamin C, iodine, hydrogen peroxide, and starch. If you do a search on the internet, it will turn up multiple (safe) ways of performing the experiment.
Elephant's toothpaste geyser. Break apart molecules with dish soap, food coloring, and hydrogen peroxide. Unfortunately, you need a stronger solution than what you can buy in the store to cause this kind of reaction, so you will need to search online if you want to make a crazy mess. If you just want a normal mess, you can use the store bought stuff..
This video shows the equilibrium principles involved in the blue bottle demonstration of the catalytic oxidation of glucose. In short, you can watch blue water turn clear and then blue again just by exposing it to oxygen. Pretty cool.
Here is another bit of fun that you can have with liquids (even though it's not really a chemical reaction). Ultimately, the liquids stack in layers because each liquid has a different density. You can do this with dark corn syrup, dish washing liquid, and water with a little bit of food coloring added. It is a cool (and cheap) way to make something pretty to put on your bed stand—And it's science!
Find more amazing experiments to try at home here.