How is a graduate school application affected if an undergrad does research in fields outside of their major? I'm an undergraduate freshman in the United States majoring in physics, but I am also interested in several other fields of research. I find many questions in biology and geology interesting. I'd like to explore mathematics. There are questions about materials that would be answered through research in chemistry, and there are questions in astronomy and cosmology that I'd be interested in getting involved with. 

However, there are only so many opportunities to do research as an undergrad. Would it be limiting at all when applying to grad schools for most of your research experience to be outside of your graduate field of study (physics)?
When looking at graduate applications, the fact that a student has done a some research is much more important than the content (or even the field) of the research.  It probably does not even matter much whether the people reviewing your application even understand your research.  The key point is to have a one or more strong letters of recommendation from your research supervisor(s).  Many research skills transfer relatively well from one field to another, and faculty letters than can attest to your skill level are extremely important to your application file.

Some professors may have a marginal preference for students who have done undergraduate research in the same area in which they pursue graduate studies.  Personally, I do not.  However, it is unquestionably better to have research experience in a relatively unrelated area than to have no research experience at all.