One really nice application of the Viterbi algorithm is map-matching, i.e. taking a GPS trail and "snapping" it to the road network to determine the actual route taken. It's difficult because GPS trails are often sparse and noisy, so you can't do something simple like "project onto the closest road segment". If you take the "states" of the model to be road segments and derive the transition probabilities from the shortest route between segments, you can apply Viterbi and get a very accurate result most of the time. Of course, calculating shortest routes involves Dijkstra, another famous dynamic algorithm.