What hard/technical skills are most important for Firefighter/Paramedics?

Identifying the most important technical skills is rather dependent on the department and position being sought. Required skills are usually set by regulations, SOGs, or SOPs, so identifying those as 'most important' misses the point. They're a minimum job requirement. However, understanding of and adherence to established standards and training is absolutely critical! Emergency situations are not the place to wing it. Learning to 'read' a fire or EMS scene, learning to assess threats and evaluate resources and options quickly and accurately, and learning to apply resources effectively to minimize loss and maximize life and safety are as essential to a career as to how to connect a hose, climb a ladder, or start an IV.