My hands-down favorite method for beginners (right now) is Piano Safari, created by Katherine Fisher and Julie Knerr. Two years ago, I started teaching some beginner students, and kept running into the same problems with all of my beginners. (Now, some of it might have been my teaching... but not all). Most of my students struggled with remembering notes names on the staff, playing hands together, and just in general their music moving ahead too quickly. Since they were (and still are) young and impatient, they did not want to spend weeks learning music, but if I moved on too quickly they would soon get lost.
(Disclaimer: I think piano lessons are great for teaching patience and diligence, but that wasn't the ONLY thing I wanted to teach!)
One method book that I was using expected them to memorize a few new notes each week and it just wasn't happening, even with lots of review and games in their lessons, flash cards at home, and other incentives. So, I was on the search for something new. I read articles, blogs, looked into books, and somewhere during my quest to find the "perfect" method book I found Piano Safari. Everything I read about it made so much sense that I loved it without even seeing it. Then I found out the authors were re-writing the books and I had to wait almost a whole year to get one in my hands!
Fast forward to now, and I am happily using this method with my students. The students who had problems with rhythms love doing the sight reading every week with modified Kodaly syllables. The students who came to me week after week not remembering their staff now accurately identify their starting notes with confidence. Most of my students enjoy learning to play pieces hands together by rote and watching the reminder videos during the week. (As a general rule, I'm not too into rote teaching, but this method is changing my mind a little). And the techniques represented by safari animals are great! However, I've found that my students get tired of practicing them week after week to get them just right.
Now, I'm sure Piano Safari's teacher handbook (which has great teaching ideas, by the way) has something to say about this, but here is my solution: technique remixes. I've been writing technique review sheets so students can play through them as a warm up each day and in their lesson. This way they are still practicing the same thing, but have it presented in a new way, and have a piece of paper to take home to remind them what they are doing. It's a win-win!
(The Piano Safari authors are working on their second book right now. I hope they finish in time for me to continue using their books!)
UPDATE 4/23/13: After trying this with a student, I found that the alternating hands (on the first and last line) was difficult for students to understand as it moved back and forth more quickly than most of their music does. Since this is meant to be a review, and not super hard, I edited those lines to make it a bit easier.
UPDATE 6/12/2014: I've actually moved away from using these review sheets, despite the popularity of this post. I tried a new approach with a few students and it worked much better. I treated each technique as a warm up that we did at the beginning of each lesson. I continued to do them and assign them until they were perfected. This way the student got into the habit of playing a warm up every time they practiced, and since we treated them differently than songs they weren't as antsy to move on.