Preferred method: Piano Adventures (Faber & Faber)
Though saxophone is my primary instrument, most of my students are piano students due to the popularity of the instrument, especially at a young age. I have played piano since I was four years old, with guidance from my father, and have also taken lessons on pipe organ to further my keyboard skills.
Since I mostly teach beginners, I usually just use the Piano Adventures series by Randall and Nancy Faber. I prefer this method because it retains a classical instruction core but also introduces other styles, from jazz to rock to world music. With the variety of music out there today, students often want to learn to play their favorite pop tune or Christmas song on the piano, and the Piano Adventures series provides exactly that. The series also gets the student moving around on the piano sooner than other methods like Alfred's piano library, giving the student a stronger grasp of the entire instrument at an earlier level.
I certainly do not limit myself to those books, though. I have used the Alfred series on occasion, and with some of my more advanced students I have used Hanon exercises or contest-level publications of well-known piano pieces. I am always willing to honor the requests of my students and their families, as well.