Michael P. Cohan writes:
The exercises are carefully designed to (1) strengthen the weak fingers of the hand (3-4-5), and (2) teach patterns of notes that recur not only in classical music but in melodies of all types of music. Each exercise varies in a manner that rests the fingers worked on in the previous exercise, so you can play through a series of them without overly tiring out your hands. For this reason they work great as warm-ups.
The exercises can get very monotonous and they drive my younger sister up the wall. But they work.
Eric C. Sedensky's opinion:
Promise yourself to play something lively and fun after you plunk at these exercises for a half hour or so, and listen as your playing begins to even out and your hands take you to musical places you've never been before.
Is Hanon useful? Yes and no. The most useful advice I would give anyone looking at this method is never to heed the "Concluding Remarks" that appear at the end of Part III:
Now that the student has completed this book, he[sic] should be familiar with the most important technical difficulties. But in order to retain the benefits of these exercises and become a real virtuoso, he should play through the entire book at least once a day. An hour is required to do this.
All 60 exercises? In one sitting? Preposterous! That's a surefire recipe for tendonitis, especially with the dreaded tremolo exercise right at the end. And these days very few pianists have an hour to kill doing Hanon every morning before they start their repertoire.
My recipe for Hanon: concentrate on the first twenty exercises, but play them in all 12 keys with various rhythms. Do them 10-15 minutes a day in addition to other piano technique, such as can be found in the RCME curriculum.
Other interesting editions of Hanon include Boris Berlin's edition, including different rhythms to liven up things and the Peters edition, which I have nicknamed Extreme Hanon. There are so many variants in the Peters Hanon that I doubt if any pianist could ever get through them, and some are so difficult they will make you weep.
At any rate, the main reason I assign the first 20 of the Hanon is that traditional piano technique (scales, chords, arpeggios, etc) often neglects the 5th finger, which is mostly used only once in a pattern, if at all. Adding the Hanon to your practice regimen evens out the action of the fingers and adds some spice to technical practice (especially if you eventually learn the first 20 in all 12 major keys, an adventure rife with surprises and rewards).