The Squat is a universal movement that all physical art forms share in one form or another. Various forms of the squat are used in martial arts, combat, dancing, yoga, qigong, gymnastics, aerobics, and of course, weight training--it is used as an exercise to build strength and stamina, to generate force, to help find ones center, etc.
The legs are to the body what the trunk is to a tree. The stronger the tree trunk is, the more the tree can grow, develop and branch out. Strong legs are the foundation of a great physique--aesthetically and functionally.
When I was learning kung-fu, the instructor would have us practice the basic stances for months before we could start learning forms and techniques. Spending countless hours in a horse stance (which closely resembles a wide stance squat) for example, helped us build the lower body strength and stamina required to execute the techniques efficiently. Without leg strength, our hand strikes would have no power behind them no matter how strong our upper body muscles were.
Ask anybody who can bench 500 pounds, and they will tell you that leg drive is a huge factor in successful pressing. The kinetic force generated from the legs transfers to the upper body, resulting in a stronger press--this applies to most athletic movements as well.
As strength coach Mark Rippetoe puts it:
“There is simply no other exercise, and certainly no machine, that provides the level of central nervous activity, improved balance and coordination, skeletal loading and bone density enhancement, muscular stimulation and growth, connective tissue stress and strength, psychological demand and toughness, and overall systemic conditioning than the correctly performed full squat.” - Mark Rippetoe
If you have a healthy functioning pair of legs, go squat!