Given a directed acyclic graph with labeled vertices, we consider the problem of finding the most common label sequences ("traces") among all paths in the graph (of some maximum length m). Since the number of paths can be huge, we propose novel algorithms whose time complexity depends only on the size of the graph, and on the frequency epsilon of the most frequent traces. In addition, we apply techniques from streaming algorithms to achieve space usage that depends only on epsilon, and not on the number of distinct traces. The abstract problem considered models a variety of tasks concerning finding frequent patterns in event sequences. Our motivation comes from working with a data set of 2 million RFID readings from baggage trolleys at Copenhagen Airport. The question of finding frequent passenger movement patterns is mapped to the above problem. We report on experimental findings for this data set.