The deployment of millimeter-wave (mmWave) cellular systems in dense urban environments with an acceptable coverage and cost-efficient transmission scheme is essential for the rollout of fifth-generation and beyond technology. In this paper, cluster-based analysis of mmWave channel characteristics in two typical dense urban environments is performed. First, radio campaigns are conducted in two identified mmWave bands of 28 and 39 GHz in a central business district and a dense residential area. The custom-designed channel sounder supports high-efficiency directional scanning sounding, which helps collect sufficient data for statistical channel modeling. Next, using an improved auto- algorithm, multipath clusters and their scattering sources are identified. An appropriate measure for inter- and intra-cluster characteristics is provided, which includes the cluster number, the Ricean -factor, root-mean-squared (RMS) delay spread, RMS angular spread, and their correlations. Comparisons of these parameters across two mmWave bands for both line-of-sight (LoS) and non-light-of-sight (NLoS) links are given. To shed light on the blockage effects, detailed analysis of the propagation mechanisms corresponding to each NLoS cluster is provided, including reflection from exterior walls and over building corners and rooftops. Finally, the results show that the cluster-based analysis takes full advantage of mmWave beamspace channel characteristics and has further implications for the design and deployment of mmWave wireless networks.