As you have indicated, the formation of a precipitate is a good indicator of a chemical reaction. However, it is not the only indicator, since it depends on the formation of a product that is insoluble in water or whatever liquid you are working in. One workaround is to try to predict reaction products and see if you can alter the solution to create a precipitate. You can adjust the pH and check for precipitates; this link will walk you through the steps for doing so.
Other signs of a reaction occurring include temperature changes, bubbling or fizzing which indicates gas generation, color changes, and odors.