I personally think, the Cold War end is the most noteworthy thing to celebrate because of the horrible things that were avoided, but I am always confused which day would make the most sense.
The Cold War wasn't an actual war, yet a nickname for the tension between the Soviet Union and the United States of America in the 20th century, though some of that tension still exists.
However, the "war" focused on the specific period of after World War II all the way to Ronald Reagan's presidency.
Alot of people would classify the date of the Cold War's end when the USSR collapsed (I would personally also mark that).
The Berlin Wall's fall on November 9, 1989 also marked a significant time in which America began to "win" the Cold War.
If you want me to tell you the factors of the Cold War ending, I could, but I'll answer your question directly.
On the 25th December 1991, the leader of the Soviet Union, Mikhail Gorbachev, resigned as President of the USSR and on the same day the flag we now know as the Russian flag was raised in Moscow. The collapse of the Soviet Union and new independent Russia (and 14+ other countries) personally, for me, marked the end of the Cold War.
Source(s): http://www.ushistory.org/us/59e.asp
http://www.coldwar.org/articles/90s/fall_of_the_soviet_union.asp