I have heard that Tish'a B'av is a date on which many bad things happened to the Jewish people, and that is why we mourn on that day.
What are they? (Sources please...)
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Several events are listed in chapter 13 of Megilat Ta'anit:
בתשעה באב נגזר על אבותינו שלא יכנסו לארץ וחרב הבית בראשונה ובשניה נלכדה ביתר ונחרשה העיר
The fifth event lacks details. The parallel account in the Mishnah (Ta'anis 26b) is also vague on this fifth event. Rambam, however, provides us with some details:
ותשעה באב חמשה דברים אירעו בו נגזר על ישראל במדבר שלא יכנסו לארץ וחרב הבית בראשונה ובשנייה ונלכדה עיר גדולה וביתר שמה והיו בה אלפים ורבבות מישראל והיה להם מלך גדול ודמו כל ישראל וגדולי החכמים שהוא מלך המשיח ונפל ביד הרומיים ונהרגו כולם והיתה צרה גדולה כמו חורבן בית המקדש ובו ביום המוכן לפורענות חרש טורנוסרופוס הרשע את ההיכל ואת סביביו לקיים מה שנאמר ציון שדה תחרש
On the Ninth of Av, five tragedies occurred:
It was decreed that the Jews in the desert would not enter Eretz Yisrael;
The First and the Second Temples were destroyed;
A large city named Betar was captured. Thousands and myriads of Jews inhabited it. They were ruled by a great king whom the entire Jewish people and the leading Sages considered to be the Messianic king. The city fell to the Romans and they were all slain, causing a national catastrophe equivalent to that of the Temple's destruction.
On that day designated for retribution, the wicked Tineius Rufus plowed the site of the Temple and its surroundings, thereby fulfilling the prophecy [Micah 3:12], "Zion will be plowed like a field." (Chabad.org)
Here are additional events to the ones already noted in other answers
Expulsion from England (1290): The Jews of England were expelled by King Edward I (chabad.org)
French expulsion (1306): The Jews were expelled from France (from here)
Spanish Expulsion (1492): The Jews of Spain were expelled by King Ferdinand and Queen Isabella on the 9th of Av of 1492, terminating many centuries of flourishing Jewish life in that country. (see here #6)
Opening of the Treblinka concentration camp (1942) (from here)
Mass deportation of Jews from the Warsaw Ghetto (1942) (from here)
Deadly bombing of the Jewish community center in Buenos Aires, Argentina which killed 86 people and wounded some 300 others (from here)
Disengagement from Gaza (2005) (from here)
Wikipedia here has more references for these events.
Heinrich Himmler received the formal command from the Nazi Party to initiate the Final Solution, an order which resulted in millions of Jewish deaths. This happened on Tisha B'Av in 5701, which corresponds to August 2, 1941 on the Gregorian calendar. (Source)
This article notes two events not listed above:
1095: First Crusade declared by Pope Urban II. 10,000 Jews killed in first month of Crusade. Crusades bring death and destruction to thousands of Jews, totally obliterate many communities in Rhineland and France.
1989: Iraq walks out of talks with Kuwait.