for me it's memorizing. i have loads of music stored in my brain that i can play at will. i only took 3 months of piano lessons then quit, then 3 years later i started to teach myself so i cant sightread so i go through and learn it note by note by memorizing.
I can't memorize anymore. So I have to have the music. Some unfortunate accidents resulting in head trauma are what I attribute it to. I couldn't even play twinkle twnikle little star. I could figure it out and play it, but I'd have to do it all over again tomorrow.
If you want to memorize, you must be 100% sure you must be absolutely sure that you know the piece off by heart, otherwise that 1% chance just might kill you during your performance
Memorizing. Not only on piano, but on any other instrument. It makes it seem so much more like music to me instead of a bunch of little black notes on a piece of paper.
I tend to do it like Dan, but of late I've been trying (key word there) to play some more challenging pieces so I've been forced to read the music. I know I'll never be able to sight read and play Kieth Emerson's "Karn Evil 9: 2nd Impression", but I have fun.
I disagree that memorizing is more "musical" than having a score - memorized pieces will mutate with time, but a score is constant, and contains far more information than "play the riff like this"...but there is a point where relying on the printed music (especially in pop and jazz) can be stiffling.