In addition to various elementary repertoire and technique books these are a few of the materials that I find useful for the specific purposes that they focus on:

Hanon, The Virtuoso Pianist in Sixty Exercises by C. L. Hanon - Pure technique. This volume was designed to strengthen the naturally weak pinky and ring fingers and develop finger independence. In addition there are exercises for scales, arpeggios, repeated notes, and scales in common intervals up to an octave. Often if I am having difficulty with a passage I will play a relevant section from Hanon. When I return to the passage the technique has been reenforced and I can play it.

Learn to Play the Alfred Way, Jazz Piano by Roger Edison - The clearest book I have found to date for learning to improvise in the jazz style. This book assumes the student already knows how to read play at an intermediate level. It begins with rhythmic concepts such as anticipation and retardation and then progresses through melodic embellishments such as neighbor notes and passing tones. About half way through it delves into chord construction and progressions and techniques for improvising new melodies over them. Although many books cover this same material I like this one for it's logical progression and thoroughness, particularly with extended chords. Also, it uses idiomatically correct left hand voicings and smooth voice leading instead of the typical clunky root position chords so common in this type of book, so the examples sound good and are fun to play.

Notebook for Anna Magdalena Bach by J.S. Bach and others - A classic of beginning to intermediate classical repertoire.

The Jazz Theory Book and The Jazz Piano Book by Mark Levine - These books cover the same territory as the Roger Edison book but in much greater depth and in a more theoretical manner. In particular the areas of reharmonisation and chord / scale relationships, especially with altered chords, are covered in much greater depth. These books are really aimed at advanced or college level students. One area where these books really shine is in their extensive use of examples from actually recordings. If you were to go and buy all of the recordings referenced in the books you'd have a very good and stylistically representative jazz collection.

Portable CD Player, Tape Recorder, Minidisk, etc., and Your Ears - The value of listening to yourself play on a recording should not be underestimated. Likewise, playing along to recordings and doing transcriptions are the best ear training available. I suggest something with speakers that can sit on top of the piano, as opposed to a walkman type device with headphones. In my experience it is easier to hear both yourself and and the recording if the sound is coming from roughly the same place.

Your Voice - A common mantra among jazz musicians is "if you can't sing it, you can't play it". Well I can play chords but I can't sing them. Still, the idea has merit. Singing a phrase can cement it in your head and inform your phrasing better than just about anything else.