I know there's a few honor societies that are recognizable and helpful for graduate admissions. I got invited to join Pi Mu Epsilon, which identifies itself as "the U.S. honorary national mathematics society." Apparently one qualifier is "Undergraduate students who have completed at least the equivalent of two semesters of calculus and two additional courses in mathematics, at or above the calculus level, all of which lead to the fulfillment of the requirements for a major in the mathematical sciences. In addition, such students must have maintained a grade point average equivalent to that of at least 3.0 on a 4 point scale, both for all courses that lead to fulfillment of requirements for a major in the mathematical sciences, and also for all courses that lead to fulfillment of requirements for an undergraduate degree." It seems like there's not much benefit to joining since everyone in graduate school will have at least a 3.0. You do need to be nominated, though. How helpful would this be for a graduate application?