It's weight-lifting gospel: always train with a full range of motion. A Google search reveals conflicting views and ambiguous talk of 'research'. What is full range of motion, anyway? Do you really need it?
Part of the problem with the concept of 'full range of motion' is that it's not always clearly defined. For example, does it mean touching the barbell to the chest in a bench press, then fully extending the arms? Or is it better to use a specialized bar that allows the hands to pass below the chest for even more range of motion? Is a squat to parallel (like a powerlifter would do) a full range of motion, or must it be 'ass to grass' (like an Olympic weightlifter would do)? Does a dumbbell lateral raise require you to start with your hands at your sides and touch your knuckles overhead, or is simply raising the dumbbells to shoulder level (the most common method of performing the exercise) a 'full range of motion'?
What's the goal?
Whether it's important to train with a full range of motion depends on the goal of your training. If you're training for a strength or performance oriented movement that requires a full range of motion, then of course it's important to train that range accordingly. An Olympic weightlifter, for example, absolutely must train through a full squat from below parallel to full extension at the top because that is what their competitions require.
But the idea of 'full range of motion' is generally applied to bodybuilding-style movements (isolating muscle groups), and that's where its efficacy gets a bit murkier. Hypertrophy (muscle size) requires time under tension under relatively high loads. As you move through the range of motion, the 'strength curve' of the muscle varies, as does mechanical advantage. In a bench press, for example, the bottom third of the movement is heavily pectoral-dominant, while the top third is more triceps-dominant as well as providing mechanical advantage via extension of the elbows. If the goal of the bench is a competitive environment, such as powerlifting, then training through a full range of motion is valuable because competition will require full depth and extension. But for a bodybuilder trying to develop the chest, does it make sense to train the top, triceps-heavy portion of the movement?
In these cases, it might be more effective to keep continuous tension on the target muscle(s) by using a truncated range of motion. This isn't a fringe idea, either; it's employed by a number of prominent bodybuilders including Jason Huh, Branch Warren, and current Mr. Olympia Phil Heath.
It may also be beneficial to target different portions of the range of motion depending on the strength curve. A muscle is weakest when fully shortened, so early in the workout you can try training the shortened range of motion. Later, as the muscle fatigues, you can train the stretch portion of the strength curve. You could even do them in succession; for example, try doing a compound set with spider curls (top 2/3rd of the range of motion only) immediately followed by incline dumbbell curls (bottom 2/3rd of the range of motion). The training in the fully shortened position will engorge the muscle with blood, and make for a subsequently ultra-painful stretch. This kind of staggered range of motion training is advocated by another pro bodybuilder and trainer, Ben Pakulski.
I'm a believer that there's no foolproof way to train. Some people use a full range of motion and get great results. Personally, when training for muscle size, I prefer to use a shorter range of motion. I used controlled (not explosive) repetitions and, because of the shorter range, usually employ higher repetitions — in the 12-20 range — to maintain time under tension. Make no mistake, this is a brutally difficult method of training. If you're in a rut, give it a try — you might find that 'full range of motion' isn't all it's cracked up to be.