Superhydrophobic surfaces with a monostable Cassie state possess numerous interesting applications in many fields, such as microfluidics, oil-water separation, drag reduction, self-cleaning, heat dissipation, and so on. How to guarantee a monostable Cassie state of a superhydrophobic surface is still an interesting problem. In this paper, considering the influence of external interferences that may induce the possible wettability transition, the whole wetting process of a droplet on a trapezoidal micropillar-arrayed superhydrophobic surface is divided into six possible stages. Both the Gibbs-free energy in each stage and the energy barrier between adjacent stages are obtained and analyzed theoretically. It is interesting to find that the finally stable wettability of a trapezoidal micropillar-arrayed superhydrophobic surface significantly depends on the apparent contact angle of the lateral surface of a single micropillar, which can be divided into three regions from 0 to 180 degrees, corresponding to the Wenzel state, metastable Cassie state, and monostable Cassie state. Furthermore, the size of each region is explicitly related to and can be well-tuned by the geometry of microstructures. Such a wettability classification is well verified by a number of existing experimental results and our numerical simulations. As a relatively general case, such a trapezoidal micropillar-arrayed superhydrophobic surface can also be conveniently degenerated to the triangular or rectangular micropillar-arrayed surface. All the results should be useful for the precise design of functional surfaces of different wettabilities.