If you had any doubt research is an important element of any residency application and even more so if it is an application of an FMG/IMG. This is since research is perceived as clear cut evidence of a true, long term, interest in the specific field.
There are several levels of research of course. While some people write a short case report, others participate in year long projects that examine complex questions in their respective fields. Still other have a repertoire of projects under their belt. As anyone can deduce, the more significant one's research experience the more useful it is as a supplement to the residency application.
Despite the above, research is not a necessity in most fields and many American graduates do not have significant research projects in their resume. When it is necessary is if you're going for a competitive specialty. Many American graduates going for these specialties have research and so at the least you must be on par with them. If you want to really blow the program director out of the water then become an expert in your field before you even apply by participating in several research projects. This will make it clear that before the acceptance committee is a serious applicant who has both a true interest and significant research experience in the field.
As a final statement, one can say that as a foreign medical graduate research is always recommended.
Research & Residency
Application & Interviews