Which courses should I take in college if I want to work as a researcher after I graduate?

In college you should take a lot of science/math classes: biology, biochem, physical chem, calcI,II, etc, and any genetics/genomics classes offered. The genetics classes might be more like seminars than large lecture classes because the field is constantly evolving and its difficult to keep a textbook updated. More importantly, you should find a laboratory that you like and work as a lab/research asst. The sooner you find one, the higher possibility you will be able to be part of a publication (not always possible in undergrad). If you do this you can likely apply directly to grad school whereas if you have no lab experience you will have to work as a technician for a few years before applying to graduate school. It might behoove you to choose a college that is affiliated with a medical school which may have more interesting and translational research, but that is purely up to what you find interesting!

I would just like to add that although you want to do research related to cancer this can take many different forms. Everyone else on this post has provided great advice.
I just want to mention that you may be looking at cancer in a pharmacology lab, a genetics lab, a physiology lab, a pathology lab etc.
The disease is multi-faceted therefore you can choose to explore different aspects of cancer.

Perhaps, it also may not be a bad idea to volunteer for cancer research society (many different positions available). Another idea would be volunteering in the hospital engaging with cancer patients and helping with various social activities. This may help you in the future. Just an idea if it appeals to you.

There is nothing like experience, so take classes that have a heavy laboratory component, such as chemistry and biology. I actually did breast and ovarian cancer genetics research for a while, and my qualifications came from my lab experience. As Jamie said, find a professor on campus that is doing interesting work, try to get into their lab for an independent study/research project, and that will give you a taste for whether you want to pursue this path long term. As a heads up, you need to have lots of patience, as sometimes the experiments can take a long time to conduct. There is a lot of research being done on various cancers, so there are all kinds of ways this career could play out.

Make sure you are having fun when you are doing the coursework. The introductory and intermediate courses, while important for the basics, are not nearly as exciting as the projects you're involved with as an actual researcher, and I have seen a lot of people who would have made great researchers, never get there because they are discouraged by their college courses.

What this means: don't overload and overwhelm yourself with too many science courses, thinking that you need to rush to accomplish your goal. Major in it but don't live and breath it when you are still in college. Then I would actually suggest taking up a position as a technician before applying to graduate school to see if you still like doing research. Otherwise, you'll drive yourself crazy and burn out.