Thermal solidification processes are an important concern in today's manufacturing technology. Because of the complex geometric nature of real-world problems, analytical techniques with closed-form solutions are scarce and/or not feasible. As a consequence, various numerical techniques have been employed for the numerical simulations. Of interest in the present paper are thermal solidification problems involving single or multiple arbitrary phases. In order to effectively handle such problems, the finite element technique is employed via enthalpy formulations and adaptive time stepping approaches to accurately and effectively track the various phase fronts and describe the physics of phase front interactions and thermal behavior. The automatic time stepping approach uses the norm of the temperature distribution differences between adjacent time step levels to control the error, where the scale of the norm is automatically selected. Several numerical examples, including single and multiple phase change problems, are described.