Sure, full range of motion makes the most sense most often. But under certain circumstances, partial movement is actually more effective than full range of motion. Here are three examples:
1. Use partials to strengthen a specific part of the range of motion.
This is based on the principle of accentuation, which means doing an exercise only in the range of motion you wish to strengthen. This method can be used in powerlifting to strengthen a sticking point in a movement. It's also common in athletics. In track and field, quarter or half squats are popular because they overload the specific range of motion required in their sporting activities. Once you've built a solid base of overall full ROM strength, overloading the specific range of motion can transfer to performance.
2. Use partials to create a large overload for strength gains.
Using supramaximal weights can lead to strength gains over the full range of motion by desensitizing the Golgi tendon organs and strengthening the stabilizers and fixators as well as the prime movers.
Just because you're doing a partial movement doesn't mean that the muscles aren't working. You're still placing the muscles and tendons under a tremendous load that can strengthen these structures. It also helps you psychologically: handling supramaximal weights will make maximal weights feel lighter. Thus you'll have less psychological inhibition when attempting heavy lifts.
3. Use partials to increase muscle loading and build muscle.
This is the "keep the muscles under tension" approach used by bodybuilders. This concept is about utilizing a multi-joint exercise to isolate a specific muscle. No, you aren't truly isolating it since other muscles will come into play, but the target muscle will be put under constant tension similar to an isolation exercise. The main difference is you'll be able to use more weight.
Do this by keeping reps only in the range of motion where the target muscle is doing most of the work by itself. You want to avoid going into the "transition" zones where other muscles start to take over so that maximum tension is maintained on the target muscle. Here's an example.
Using Partials with the Shoulder Press
Notice he's only doing the mid-range portion of both the behind and front presses –stopping just before the triceps would take over. The best rep style to use is "low momentum." While you aren't trying to go slow, you try not to accelerate the weight to a high degree so that you avoid creating momentum that would release some of the tension placed on the muscle.
Doing only partial lifts is dumb, but properly used partial movements certainly have their place in a solid training program. Don't let the 135 pound exercise purists tell you otherwise.