Physical Danger
Most of greenskeeping boils down to cutting stuff. Cutting stuff means cutting tools, and cutting tools mean cuts. If you're lucky, that means a scratch on the arm. If you're not, well...just make sure you're using your equipment safely.
Chainsaws, mowers, and trimmers can all cause great harm if not respected, as can falling tree branches and the occasional rogue golf ball. (Fore!) As with all professions that require dangerous tools, the trick is to never get complacent. If you always keep in mind that you're six inches away from massive swirling blades, you'll probably make it to the end of each day with all your limbs and digits intact.