Machine unlearning, the process of efficiently removing specific information from machine learning models, is a growing area of interest for responsible AI. However, few studies have explored the effectiveness of unlearning methods on complex tasks, particularly speech-related ones. This paper introduces UnSLU-BENCH, the first benchmark for machine unlearning in spoken language understanding (SLU), focusing on four datasets spanning four languages. We address the unlearning of data from specific speakers as a way to evaluate the quality of potential "right to be forgotten" requests. We assess eight unlearning techniques and propose a novel metric to simultaneously better capture their efficacy, utility, and efficiency. UnSLU-BENCH sets a foundation for unlearning in SLU and reveals significant differences in the effectiveness and computational feasibility of various techniques.