Empirical channel modeling is necessary for the deployment of the fifth-generation (5G) millimeter-wave (mmWave) cellular system in actual environments. In this paper, cluster-based analyses of mmWave channel characteristics in two typical dense urban environments are performed. First, radio propagation measurement campaigns are conducted at two primary 5G bands of 28 GHz 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 to collect sufficient data for statistical channel modeling. Next, using an improved autoclustering algorithm, multipath clusters and their scattering sources are identified. Mapping results show that multiple reflections from exterior walls and diffraction over building corners or rooftops enhance the coverage for non-line-of-sight (NLoS) links and the influences of these propagation mechanisms are intuitively embodied as changes in the topologies of deployment environments. Finally, an appropriate measure for cluster-level channel characteristics is provided including cluster number, Ricean K-factor, root mean squared (RMS) delay spread, RMS angular spread, and their correlations. Comparisons of these parameters across two mmWave bands are also given. The measurement and modeling results shed light on a fully understanding of mmWave channels in dense urban environments across multiple bands.