I don't understand why members are recommending Hacks and pendulums - those are squats and he specifically said without doing squats regularly.
Barbell squats are not a magic exercise and other forms that don't involve a barbell are just as much squats. In fact, barbell squats are one of the worst hypertrophy movements for most guys. I have one of the best sets of quads on this board and I built them on a plate-loaded Free Motion Hack squat.
To answer the original question, I don't feel you need to squat regularly to build good legs. Your muscles don't know what movement you're doing, what implement you're doing it with, or how much weight you're using - they only know how hard they work. With all the leg press variations out today a good set of legs should be very doable without squatting.
2 more points on the original post:
- If 10 sets of 20 reps with 500lbs. isn't fatiguing your legs to a good degree then you likely don't know how to leg press with your leg muscles
- You need a lot more weight if you want to build your legs with a leg press - for perspective, my heaviest sets of leg press each week are 1,000+lbs. for 10+ reps.