Full Range of Motion vs Partial Reps

You see them every time you go to the gym - the guys and gals who cheat. Not on each other, mind you, but on their workout. They arch their back as much as a crossbow during the bench press. They heave the weights upward during the curl. And most of all, they only perform partial motions during almost all of their lifts.
Partial lifting has its place, but it should never be employed as a constant. That is, a partial range of motion, particularly using a power rack, can be used to help you move past a sticking point. There is an entire scheme predicated on this approach, called power rack partials. However, such an approach should always be cyclical and never become a mainstay in your training.
For the best results, it is vital to employ a full range of motion when lifting. That's because a moderated range of motion only partially develops the muscles. And for bigger muscles, you want fully developed muscles. The wider a range you can put the muscles through under a work load, the better. For instance, when you go all the way down in the squat, you engage your hamstrings much more than does a partial range of motion.
Full range of motion training is especially important for the guys who want to build an athletic body. To perform all out, you have to train all out. And the broader a range you can engage the muscles, the more fiber recruitment you can spark, and continue to hold under tension.
Of course warming the muscles up prior to a full range of motion movement is vital so that the muscles are ready for the challenge. After the muscle is warmed up in a full range, put it under a workload for the full range. A full range of motion activates more fibers and keeps those fibers firing longer. That is, the muscle has more "time under tension" - one of the key factors for facilitating growth.
Some people default to partial range of motion because it is simply harder to perform a full range of motion. But it is also better to get into that full range of motion. Massive muscle recruitment and time under tension do matter, both for building muscle and improving the athletic capability of the human body. Aside from some specific cheating cycles, stick with a full range of motion approach to your training as your base approach.