my guess:

80% hayır
15% yok
5% other ways

tamam. Thank you Ikicihan

We also use one voice for no. It is "cık". But we dont read it. it is actually just a voice which i can not describe well now.

It is like you use air which is already in your mouth and try to say "nt" by drawing air into the mouth. Sorry, my english is not enough to explain it. But i am sure, we Turks use this "no" more than "yoo".

Eyebrows are also raised at this time

cık cık cık.. I´ll try to find videos on youtube. Maybe I find one...  (: Thank you to all of you ♥

well for the time I spent in Sultanahmet and would have the shop keepers trying to get me in their shops, just saying yok seemed to be enough to get my message across or domates yok when ordering lahmajuun.  Never got tomatoes.

The backward tilt of the head with the click of the tongue I used when in a conversation and they would say something that would merit a "no way"

The easiest way to explain the no head movement is like in Brittain when someone tuts at you.  I know this because I almost had a big argument with someone when he used this when I offered him a beer, he had used this form of a no reply several times and I, thinking he was being judgemental about my beer drinking, was about to say, "Tut at me one more time...." when a mutual friend explained its meaning.

lol , well I´m not british so I don´t know what "tut" means

how to pronounce "cık" . try to say t in reverse way. say it inwards, not to outwards, i mean your air flows backwards when your tongue end touches "damak". it is a sound mixing of t and c (j in english) it is neither a letter nor a word, so it has a unique pronunciation and exremely informal.

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finally i found it somewhere on youtube but to my surprise nothing turkish there. i think some other countries use it, too.
if you say it one time it means "no",
if you say it three or more time as in the following example it means "it is wrong what you are doing" in turkish!

The Meaning of Tsk

http://www.youtube.com/watch?v=-imfjwhDM0A

Wow wow wow. I thought to say no you repeat the verb in the negative:

--Kitabi beğendin mi? (Did you like the book?)

--Beğenmedim. (No, I didn´t)

I remember reading that saying hayır by itself was kind of rude… Maybe I´ve been led astray. 

--Beni seviyor musun?

--(Hayır,) (seni) sevmiyorum. 

Tut mak =to hold  hold my bag ,  çantamı tut 

takım tut mak = to sport a team 

seni tuttum = i liked you

also did you mean "dut" ?  dut = mulberry

aklında tut (mak) =not to forget it

çık, ıı are not formal.

hee means yes it is not also formal