This paper studies the distributed mode consensus problem in a multi-agent system, in which the agents each possess a certain attribute and they aim to agree upon the mode (the most frequent attribute owned by the agents) via distributed computation. Three algorithms are proposed. The first one directly calculates the frequency of all attributes at every agent, with protocols based on blended dynamics, and then returns the most frequent attribute as the mode. Assuming knowledge at each agent of a lower bound of the mode frequency as a priori information, the second algorithm is able to reduce the number of frequencies to be computed at every agent if the lower bound is large. The third algorithm further eliminates the need for this information by introducing an adaptive updating mechanism. The algorithms find the mode in finite time, and estimates of convergence time are provided. The proposed first and second algorithms enjoy the plug-and-play property with a dwell time.