Most people don't realize that a lot of people who actually start working out and haven't been active for long periods of time tend to do poorly in the squat for a big reason and that's tightness. Most people have a lot of tightness in the ankles, hips, calves, hamstrings, and glutes.
A simple way to find out if you're tight is you grab a broom and do an overhead squat. If you start leaning on your toes that's a sign of tightness in your body. You'll need to start mixing in dynamic and static stretches.
Stretching goes a long way in properly executing a squat. Your back should stay quite upright as opposed to leaning forward a lot. I had that issue for a very long time and doing stretches for my ankles, calves, and hips gave me the depth I was getting but didn't make me lean forward more cause a strain in my back.
I prefer going ass to grass, so I have to make sure there is adequate flexibility to allow me to execute this without having poor technique and ruining my lower back. I don't know if anyone read the article about third world squats on T-nation but do you see how low those guys go while having their heels remain on the ground and their spines are fairly upright. Very little leaning is going on.
Here's the article and maybe you should practice those. It will relieve a lot of the tightness in many spots. It's difficult at first but it helps a lot: