The Shulhan Aruch rules that it is prohibited to tie a permanent knot on Shabbat that will last for more than seven days, even if it is a simple, nonprofessional knot. Any simple knot that will not last seven days is permitted.
One common example, which people are not aware of, is tying garbage bags on Shabbat. The simple double knot used to tie them will remain forever. Nobody ever intends to untie it, and therefore it is prohibited.
Another example is tying a necktie on Shabbat with intent to leave the knot in place, even after loosening it and removing it. If it would remain for more than a week, it is prohibited to tie it on Shabbat.
There is a scholarly inquiry regarding a case in which a person tied a necktie on Shabbat with intent of untying it on the same day, which is clearly permitted. What is the Halacha if, during the course of Shabbat, he changed his mind and decided to leave the knot of the necktie in place? Does his new intent, after the fact, retroactively render his act of tying a forbidden Melacha? Hacham Yishak Beracha wrote a length discourse on this subject, expounding both sides of the question. His conclusion is to be strict. Therefore, one should make sure to untie a necktie tied on Shabbat within seven days.
SUMMARY
It is prohibited to tie a double knot in garbage bags on Shabbat.
While it is permitted to tie a necktie on Shabbat, one must insure that he unties it within seven days.
