When I work with a new client, maximal strength is not usually one of their main goals. They mention improved body composition, muscle tone, energy, less aches and pains, and feeling better about themselves. However, when we look a little closer, maximal strength is the foundation for improving all other physical fitness qualities. Rarely, is maximal strength trained. Usually you see people 'working' various muscles. Unfortunately, they are 'working' those muscles without any improvements in their body composition or physical fitness for years.
When you improve maximal strength in many of the various lifts (deadlift, squat, press, cleans, snatches, pull-ups, etc.), you will also improve your body composition. You don't have to log hours on a piece of cardio equipment or use light weights and high reps. These methods are inferior to progressive strength training. Progressive strength training of the main lifts improves your body composition by elevating your resting metabolic rate, building muscle, and requires a significant calorie expenditure. Also, you can tolerate other types of exercise, such as running and cycling, better.
Another benefit of improved maximal strength is improved strength endurance, power, relative strength, speed strength, stability, posture, and flexibility. What does this mean? It means that training for maximal strength is a very efficient way to enhance all of these qualities. Instead of doing 'cardio' for endurance, machines for strength endurance, 'core' exercises for posture, static stretching for flexibility, you get it all with proper strength training.
Most people don't strength train properly. To enhance maximal strength, you need to use compound, multi-joint lifts (such as the deadlift, squat, clean, press, etc,). Why? Because strength is often limited by the ability to stabilizer the body, spine, and joints. Training individual body parts (biceps, abs, shoulders, etc.) fail to 'tie' stabilizer muscles, prime-mover muscles, and joints together to perform the lift. Another important principle is to practice the lifts, not 'feel the burn.' You need to manage fatigue, not pursue it to develop maximal strength. I know this flies in the face of most of the advice you hear from fitness magazines and personal trainers, but then again, if you follow their advice you really won't get very strong.
So, if you are looking for a more effective and efficient way of enhancing all aspects of fitness, you need to train for maximal strength at least a couple days per week.