Is training to failure good for muscle growth?

It's NOT necessary to train to absolute failure (where you literally cannot complete a rep) to grow muscle. 

Training near failure is a great idea, as we need sufficient exercise intensity to really elicit stimulation of the deeper muscle motor units that will lead to muscle building. 

That said, reaching absolute failure - especially through so-called "intensity techniques" like forced reps/drop sets/etc. is not necessary and can even be detrimental to your progress if done too frequently.

But we can't simply talk about the benefits vs. detriments of training to failure without talking about the exercise you're actually taking to failure.
There is a big difference between training to failure of a set of heavy deadlifts versus training to failure on a single-arm dumbbell curl.
The set of deadlifts to failure is incredibly taxing on your entire body - both muscles and nervous system. The set of biceps curls to failure is not that taxing; you can get away with many sets of curls to failure without impairing your recovery. 

The Answer: Training to failure is not necessary for muscle building... but it can be beneficial if it doesn't impair your recovery and you should do it sometimes.

One simple way to approach this is to make training to failure simply an exercise-dependent variable. 

The more demanding an exercise is on the nervous system (i.e. Squats, Deadlifts, Rows, Bench Press), you should stop short of failure (1-3 reps). Leave some in the tank, and complete another set. Stop each set when you start to lose form or when explosiveness and speed slows down.

However, in exercises where the nervous system is likely to be less taxed (i.e. curls, shoulder presses, ab work, calf work, arm isolation work), you should go to failure or even past failure on at least one set per exercise to maximize motor unit recruitment and metabolic stress. 

What I do personally:

I like to take my final set of every exercise to near-failure (if not absolute failure). 
Say, for example, we have 4 sets of dumbbell bench press (4x 10-12 reps). I'd pick a weight that I can complete 10-12 reps with 1-3 reps comfortably in the tank for Sets 1-3. The final set should be to near failure.
Above all, there is no hard and absolute rule around training to failure - simply some smart guidelines that we've discussed above. Listen to your body. If you're feeling run-down on a particular training day, don't go to failure. If you're feeling great, go to absolute failure on a few of your sets.
And, as always, remember: muscles are grown outside the gym through sleep, food, and recovery. Training is just the stimulus to get our bodies to start the growth process.
-Dr. Anthony Balduzzi
Founder, The Fit Father Project
Creator, Old School Muscle + FF30X