There are three events commonly referred to as the "Mormon
War":
The Missouri Mormon War took place in 1838 between the Mormons
and their non-Mormon neighbors in northwest Missouri. The Mormons
ended up leaving Missouri due to the hostility they faced, so I
suppose you might say that the Missourians won.
The Illinois Mormon War took place from 1844 to 1846 between the
Mormons and their non-Mormon neighbors in western Illinois. The
Mormons ended up leaving Illinois due to the hostility, so you
might say that the Illinoisians won.
The Utah Mormon War took place from 1857-1858 between the
Mormons living in the Utah Territory and the United States
Government. James Buchannan, the President of the US, had heard a
false rumor that the Mormons were planning a rebellious uprising,
and sent troops to Utah to stop it. The Mormons thought that the
troops were being sent to destroy them. The Mormons did all they
could to hinder the progress of the troops and then packed up and
moved south out of the path of the army. Eventually, the 'war' was
won by negotiation, the Mormons agreed to allow the troops to stay
in the territory, and the troops agreed to leave them alone unless
they posed a threat to the nation.
