Search-based motion planning has been used for mobile robots in many applications. However, it has not been fully developed and applied for planning full state trajectories of Micro Aerial Vehicles (MAVs) due to their complicated dynamics and the requirement of real-time computation. In this paper, we explore a search-based motion planning framework that plans dynamically feasible, collision-free, and resolution optimal and complete trajectories. This paper extends the search-based planning approach to address three important scenarios for MAVs navigation: (i) planning safe trajectories in the presence of motion uncertainty; (ii) planning with constraints on field-of-view and (iii) planning in dynamic environments. We show that these problems can be solved effectively and efficiently using the proposed search-based planning with motion primitives.