I would very much like to know of several ways people have used (or
atleast thought up of) that helped them quit smoking tobacco products
(cigarettes) which are either considered common or simply traditional.

Examples of such are :

Common:
Using Nicotine Patches/Gum - commercial method where nicotine
patches/gum are used to supply the body with the dosage which is
gradually decreased over time.

Traditional:
In Eastern Europe, they would mix a warm cup of milk with the
cigarette ashes and force the "victim" to drink it all down. The taste
and feeling after that is so disgusting that the individual pukes his
guts out after which any contact with the smoke (smell, taste of a
cigarette) makes them nauseous therefore assisting the quitting.

Thank you

I quit a 2-pack-a-day habit in 1989.

I didn't use any medicinal aids. I used my own willful stubbornness.
What worked for me was a mental image of my habit as a "monkey on my
back." Whenever I wanted a cigarette, I told myself that it wasn't
really me that wanted the cigarette: it was that damned monkey. No
matter how much the monkey pestered me, demanding to be "fed," I was
quite determined to act in my own best interests, not the monkey's. In
my imagination, I cussed at the monkey. I sneered at the monkey. I
generally gave the monkey a very hard time.

I haven't had a cigarette since October, 1989, and every time I want
one (which still happens several times a day), I imagine that monkey.
I have been starving him for a long, long time. He doesn't die, but he
has become less persistent.

Some people refer to quitting abruptly as "going cold turkey." 

In my case it was "cold monkey." ;-)

Dear ercgamble-ga,

I quit a 3+ pack a day habit in 1996. Like my colleague, pinkfreud-ga,
I still crave a cigarette at least every day, and like her I also quit
abruptly and by my own willpower, though in my case it was
cold-something, I'm still not sure exactly what!  But please have a
look at this question:
http://answers.google.com/answers/threadview?id=274004 which was ably
answered by another colleague, boquinha-ga, and to which I posted a
sincere and heartfelt comment that I underscore here, and truly hope
you will take the time read.  You (or whomever's behalf you are asking
on) are embarking on probably one of the most difficult undertakings I
can imagine -- but it IS possible to succeed.  Best wishes to you and
best of luck.  You can do it.  Really.

Warmest regards,
Byrd-ga

ercgamble...

My answer to the following question details a non-traditional
but effective approach to giving up toxic addictions:
http://answers.google.com/answers/threadview?id=333293

To ercgamble-ga

Similar to the tradtional eastern european method , my uncle tells the
story that he quit smoking by threading a hair from a horses mane into
the cigerette and smoking it. Aparently it made him that crook he has
never so much as thought of lighting up again.We will call it the
outback australian method.

Regards Jake2004-ga