How important is research experience of undergraduates in the application for graduate school? I'm planning to apply to graduate school in applied mathematics, but I do not have any research experience. The reason being is that I did not become a math major until my junior year in college. How will a lack of research experience affect my application?
Evidence showing a research experience is definitely a plus. 

However, do not get discouraged if you have none. Show in your application that you know what you want and why, be persistent and proactive and see how you can stand out in a positive sense from the rest of the applicants.