Gender separation in Judaism
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In Judaism, especially in Orthodox tradition, there are a number of settings in which men and women are kept separate in order to conform with various elements of halakha and to prevent men and women from mingling. Other forms of Judaism rarely separate genders any more than secular western society.
During prayer services in Orthodox synagogues, seating is almost always separate. A mechitza is used to divide the men and women, and often to block the view from one section to the other, though mechitza heights and opacity vary by synagogue.
Conservative, Reform, and other types of synagogues generally do not have separate seating.
Weddings and Bar Mitzvahs
At many Orthodox weddings and bar/bat mitzvahs, seating at the ceremony and often the reception is separate, sometimes with a mechitza.
In Ultra-Orthodox Judaism, many believe that men and women should not swim together. The laws prohibiting mixed bathing are derived from the laws of tzniut. This is due to concerns that bathing suits are inherently immodest, and do not meet tzniut requirements. In particular, a woman who comes dressed in a bathing suit to a pool is appearing publicly not meeting the requirements of tzniut, and a man who comes to a pool where women are dressed in bathing suits will inevitably see women dressed in this manner. Indeed, many pools within Jewish communities have separate hours for male and female swimming to accommodate those who follow this law.
Some women following the laws of tzniut will wear a long T-shirt style dress over their bathing suit that meets tzniut requirements, considering this to be sufficient for swimming in the presence of men. Men, though, are more strict about the presence of immodestly-dressed women, due to concerns over the possibility of arousal.
Currently, the majority of Orthodox Jews do not participate in mixed dancing, since dancing in most forms involves some contact between dancers.
In 2013, the Rabbinical Court of the Ashkenazi Community in the ultra-Orthodox settlement of Beitar Illit ruled against Zumba (a type of dance fitness) classes, although they were held with a female instructor and all-female participants.   The Court said in part, "both in form and manner, the activity [Zumba] is entirely at odds with both the ways of the Torah and the holiness of Israel, as are the songs associated to it." 
Many followers of Haredi Judaism have taken on the practice of separate seating while traveling. These range from abstaining to sitting adjacent to a member of the opposite sex, to having separate vehicles altogether.