Prompted by a friend and fellow pianist, here are some of my favorite warm-ups, courtesy of this book by Ernst von Dohnanyi...if you don't happen to have this excellent volume just search the hive mind and you will be rewarded. I would warn people to stay away from Nos. 1-11, however; these have the potential to damage small hands and build large amounts of unhealthy tension.
No. 12 – quarter = 92. Rotation within five-finger patterns (major/minor/diminished) w/loose wrist, combined with finger independence.
No. 14 – quarter = 72+, Scales crossing the thumb over all fingers in turn, repeated in all keys. Flexibility and accuracy across awkward crossings.
No. 15 – quarter = 72+. Accurate repetition with loose wrist while accenting each finger in turn.
Nos. 18-21 – quarter = 60-92. Major and harmonic minor scales in all keys, one beat per octave. Building velocity while remaining efficient and loose.
No. 24a-d – quarter = 72-92. Full-chord arpeggios (major/minor/diminished/dominant); building endurance while remaining free of unnecessary tension.
No. 25a – quarter = 46-60. Keyboard geography and accurate full-chord leaps (> an octave) without visual cues.
No. 26 – quarter = 72+. Double notes within a five-finger pattern (major/minor/diminished), remaining efficient in the fingers and loose in the wrist.
No. 28-30 – quarter = 60-92. Scales in double thirds, fourths and tritones.
No. 38 – quarter = 104-132. Scales in octaves. Small hands should ONLY play 1-5 rather than 1-4 on black keys.
No. 39 – quarter = 72-92. Arpeggios (major/minor/diminished/dominant) in octaves. Superb accuracy work.
No. 40 – quarter = 46-60. Double chromatic scales in octaves. More fun than any human being should be allowed to have. Practice with thumbs first. Repeat in all keys.