When I first began lifting in high school the squatting problem was exactly the opposite of what I see today. The high school gym was much like any globogym. Meatheads hitting 400 lb 2 inch squats. It looks awesome to have that amount of weight on your back but quite silly when you unlock your knees and call it a set. Zach Even-Esh tells a story in his new book "The Underground Strength Encyclopedia" in which he was the meathead in this situation and someone told him "how about you drop the weight to 135 and actually squat down?" He explains how this back handed comment actually got him thinking and lead to revelations in his training and progress.
With the fitness explosion everyone is squatting, and I mean everyone. Ask my mother her 5 RM back squat and she will be able to tell you. That would be laughable just a few years ago. But like most things in the fitness industry, the pendulum has swung entirely in the opposite direction and I see people bottoming out on a squat far past a loss in motor control, stability and making up for a lack of mobility in very curious places. You must attain proper stability and motor control where it is required, mobility where it is required, and display it in perfect unison to squat properly. This is precisely the reason I love the squat for evaluation purposes. It requires so much of the athlete, putting all ability and deficiency on display.
So how deep is too deep?
In the famous words of Dr. Stuart McGill... it depends. It depends where you're lacking, if at all. Assuming you already know the basics of how to squat, the easiest way to assess on your own is to squat down and notice when something changes. By this I mean, does your knee begin to change direction by diving inward or swaying? Does your back fall out of nueutral and begin to round, or extend further? At some point do your ankles feel like they are collapsing? Becoming cogniceint of these subtle changes will give you hints when you have reached your bottom, at least until you fix your limitation.
So now what?
Get someone to help! Find a professional with experience in functional movement assessment. This professional will be able to watch your squat and tell you where you could use some work to get deeper. Fixing your limitations could be as easy as a few minutes of manual therapy and some therapeutic exercise.