The ability to fly through cluttered environments is essential to the ecological and evolutionary success of many groups of flying animals, and has generated considerable recent interest in the bioengineered control of UAVs. Flight navigation and obstacle avoidance require exceptional aerodynamic maneuvering performance coordinated by rapid processing of visual cues. We examined the strategies pigeons adopt to fly past vertical obstacles versus horizontal obstacles, in which flight guidance is well described by steering control that targets gap openings between nearby obstacles. We observed that pigeons bias their flight direction toward larger visual gaps when making fast steering decisions. To negotiate horizontal obstacles, pigeons exhibited less steering, choosing gaps most aligned to their immediate flight direction, and experienced fewer collisions with obstacles; indicating that horizontal obstacle navigation is less challenging than for vertical obstacles. We found that pigeons adopt discrete wing morphing strategies to traverse vertical obstacles of varying gap width and navigated past horizontal obstacles with more variable wing extension, stroke plane and wing stroke path to reduce contact with obstacles. Pigeons also exhibited pronounced head movements when negotiating horizontal obstacles, which potentially serve a visual function. These findings demonstrate that pigeons exhibit a keen kinesthetic sense of body and wing position and are able to navigate vertical and horizontal obstacles using simple rules, with remarkable success, that may offer bio-inspired insight for the control of UAVs.