I like to have my clients at the gym do some squat variant almost everyday, goblet squats, back squats, thrusters, air squats, single leg squats - the list could go for a while. Obviously I LOVE to squat - its always challenging and engages SO many muscles! Here are the muscles that wikipedia says the squat works : ...thighs, hips and buttocks, quadriceps femurs muscle, hamstrings, as well as strengthening the bones, ligaments and insertion of the tendons throughout the lower body. As well as developing core strength. Isometrically, the lower back, the upper back, the abdominals, the trunk muscles, the costal muscles, and the shoulders and arms are all essential to the exercise and thus are trained when squatting with the proper form.
HOLY MOLY people. That's A LOT of muscles being worked!
With all those muscles working properly, you will be able to keep moving and functioning a lot longer in life than if you didn't train any of those muscles. Your hip mobility will continue to improve the more often you squat, your athletic abilities will improve (jump higher and further, run faster, being able to stay in that 'power position' longer!), you will also see noticeable differences in what your backside looks like! ;)
If you aren't sure that you are squatting properly, or feeling some tightness or pain, consult with a trainer, or physical therapist to help you get your body squatting properly.
Try sitting in the bottom of your squat everyday this week for 30 seconds to 1 minute at a time, next week, move to 90 seconds or even two minutes a day! Gradually increase every week the time spent in your squat and then let me know what you feel or see changes in the way you are squatting! :)