A paper by T. de Bie et al. describes one very stylish application of the Apriori algorithm for detection of transcription regulatory modules. The idea is in the smart statement of the problem, which is the following:
Find the maximal sets of genes that all share at least r common regulators, at least m common motifs, and have pairwise correlation of at least c.
It turns out that the sets of genes of interest naturally satisfy the same properties as the frequent sets in the Apriori algorithm, so it's rather easy to adapt the algorithm for this context.
I think it's a very nice example showing the wide applicability of a simple algorithm, as well as the importance stating the problem in the correct form.