what a fabulous thread.
Even though most of my reportoire is not memorized, (just picked up playing regulary again after a 25 year drought) I've played most of these songs so many times that even though the sheet is needed in front of me, I find myself using it more as a security blanket than something I really need to refer to as I'm playing.
But I am brand new to this forum, having picked up playing again after such a long spell, and I have learned so much in the last week of just reading past posts. (Bernard, you are a gem, I am already putting your memorization methods to use).
I have come to the conclusion that the extra effort involved to memorize a piece is inconsequential to the results it will give you. ONCE IT IS MEMORIZED, it is with you forever for the most part. I still have a bunch of songs that I learned as a child that are still with me today even though I haven't played them in over 20 years. They of course need a bit of touch up, but it's so weird, the notes just play without any real kind of consious thinking.
To be able to throw down and play the song from your heart , will bring out the highest form of emotion and feeling one is capable of.
I'm not saying that one cannot play a piece with great passion with the music in front of his/her face, (dammit, I challenge anybody to Chopin's Nocturne 9-2 Ebmajor for the passion I put into it, with, of course, the sheet) but I believe that the piece would have even more passion and emotion when played strictly from a confident memory. And after reading many posts here, mostly Bernard's, I am confident that I can take this relatively simple piece, (Eb major), and commit it to total memory within a weekend's time and make it part of my permanent memorized reportoire.
Bottom line is, as a soloist on a stage or whatever, it is so much more impressive to just sit there and play with nothing else, no sheet, no turner, no nothing but you in all your glory or ugliness. Everything else is a distraction to the audience and to the performer as well.
Again, I am new to this forum and relatively new to playing piano again. (took lessons religiously as a child/teen and left it alone for a long time until now, 40 years old. Been playing for last year and a half average 1 hour per day). Saw a guy 2 weeks ago from Armenia, Sergei Babayan, who played Leighton's Study Variations, Liszt's Sonata in B minor and finally Bach's Goldsberg variations, all of them, without the music of course, and I was just dumbfounded. The level that people like this have taken piano playing to, is just mind boggling. What is more mind boggling is how much our brains are capable of memorizing and retaining. I have found new meaning in my life this last month and I so look forward to the next opportuninty to sit down and PRACTICE!!!! (for memory of course).
Should the judges ding you for having the music in front of you?

??
Not at all. Like somebody else said,,,, they should have their eyes closed so that the physical distractions do not taint their judgment. But dammit, memorize it anyways. You'll thank yourself in the end.