Doing BACK squats once or twice a week is probably more than enough. However, I personally don't see a major problem with doing squats 4x a week IF you change the type of squat (there are countless types of squats besides the standard back squat with variations in bar type, bar position, foot position, depth, speed of movement, etc.), and also vary the load and / or volume. Besides squats however, you might want to consider doing some unilateral movements like lunges, split squats, or step-ups.
Also, I do think it's important to point out that you probably don't ALWAYS want to try to move the weight as fast as possible. I understand what everyone is saying and it's a good general recomendation but there are times when slower movements (or movements with brief pauses) are beneficial as a different form of training stimulus and also to develop eccentric, quasi-isometric, quasi-concentric, and isometric strength.