To squat deep, or not to squat deep? That is the question.
There are many arguments from many different people, both professionals and non, as to whether a deep squat is better than a parallel, half or quarter squat.
Well, to be completely honest, there are good points to many of the arguments.
However, when trying to decide which depth to use we must determine if the benefits outweigh the risks or not.
To give you some background, these are some of the arguments:

• Squatting to or below parallel puts too much stress on the knees.
  
• Squatting only to quarter or half depth works the same musculature as a deep squat.
  
• Squatting below parallel is unnecessary when training for athletics or daily activity.
  
• Most people are not flexible enough to squat below parallel.
  

Squatting to or below parallel puts too much stress on the knees.
Yes and no.
In healthy individuals below parallel squatting will help to keep the knee joint and its surrounding musculature strong.
That is unless you go too low.
A good determinant is to make sure that in the bottom position there is still space between your hamstring and your calf muscles.
In individuals with knee issues the amount of torque (or rotational force) and shearing forces on the knee in a parallel or below position could be too much for them.
In a healthy individual torque is good, shearing is bad.
To keep it simple, the quadriceps muscle group attaches via connective tissue to the front of shin bone.
The hamstring muscle group attaches via connective tissue to the back of the shin bone.
When you squat above or to parallel, the quads are activated much more than the hamstrings and glutes, thus pulling on the front of the shin bone creating large shearing forces in the knee, but not as much torque.
When you squat below parallel the glutes become the prime mover and are recruited more than the quadriceps.
The hamstrings become the stabilizer at the knee and are at a stretched length thus pulling back on the shin bone, minimizing the shearing affect.
The torque in this position is at its greatest.
In a subject with knee issues a quarter and/or half squat can be used in a rehabilitation setting to bring back proper strength, leading into deeper squats as strength and flexibility increase.
Squatting only to quarter or half depth works the same musculature as a deep squat.
Yes and no.
Squatting above or to parallel does work the same musculature as below parallel, however, the emphasis on which muscle groups are in use to the greater degree changes on the way down, as outlined above.
Studies have shown that:

From the standing position to a quarter depth, the quadriceps were recruited to a much larger degree than either the hamstrings or the glutes.

From the quarter squat position to the parallel position the quadriceps still had the most recruitment with an increase in glute recruitment and about the same hamstring recruitment.

From parallel to below parallel the glutes were recruited the most with the quads coming in a close second and the hamstrings third assisting the movement.

This would suggest that in healthy individuals below parallel squatting would have the most benefit in strengthening the muscles surrounding the knee and hip joints.
Squatting below parallel is unnecessary when training for athletics or daily activity.
Without regurgitating all over you what I have stated in the paragraphs above, below parallel squats require the greatest recruitment of the glutes.
In an athlete, the glutes are his/her bread and butter when it comes to explosive movement whether running, jumping, twisting, turning, kicking, throwing or whatever I missed.
In a non-athlete, the glutes balance out much of the body.
With active glutes, the upper and lower back, the shoulders as well as the knees and ankles can all stay healthy and in good position for the most part.
In terms of flexibility, for both athletes and non-athletes, in a below parallel position the hamstrings, quads and glutes as well as the calf muscles are all in a stretched position.
By squatting below parallel proper flexibility is acquired or maintained in the ankle, knee and hip joints.
Most people are not flexible enough to squat below parallel.
Many people think they are not flexible enough, but most really are.
For both athletes and non-athletes, in a below parallel position the hamstrings, quads and glutes as well as the calf muscles are all in a stretched position.
By squatting below parallel proper flexibility is acquired or maintained in the ankle, knee and hip joints.
If there is an issue with flexibility, lightweight squatting can actually be used to increase range of motion and flexibility.
Conclusion So the benefits seem to outweigh the risks when squatting below parallel in healthy individuals.
In individuals with muscular issues squatting is a good rehabilitative exercise to get them back to proper health.