This paper addresses the collision-free adaptive formation control problem for multiple unmanned aerial vehicles subject to input saturation and communication delays. First, a novel collision-free adaptive saturated control scheme is proposed using potential function and anti-windup compensator approaches. It shows that the velocity consensus and collision avoidance are realized when the directed communication topology is strongly connected. Second, the collision-free adaptive saturated control algorithm is proposed considering communication delays and collision avoidance, and it enables the asymptotic stability of the closed-loop system when the time-varying communication delays are decreasing to zero eventually. Finally, numerical simulations demonstrate that the proposed control approaches are effective, while the objectives of collision avoidance and velocity consensus are fulfilled.