Crowdsourcing has become a popular paradigm for labeling large datasets. However, it has given rise to the computational task of aggregating the crowdsourced labels provided by a collection of unreliable annotators. We approach this problem by transforming it into a standard inference problem in graphical models, and applying approximate variational methods, including belief propagation (BP) and mean field (MF). We show that our BP algorithm generalizes both majority voting and a recent algorithm by Karger et al, while our MF method is closely related to a commonly used EM algorithm. In both cases, we find that the performance of the algorithms critically depends on the choice of a prior distribution on the workers' reliability; by choosing the prior properly, both BP and MF (and EM) perform surprisingly well on both simulated and real-world datasets, competitive with state-of-the-art algorithms based on more complicated modeling assumptions.