Who knows four?
Please cite/link your sources, if possible. After Shabbat, I will:
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The number of columns (turim) of stones on the Choshen Mishpat. (Exodus 28:17)
Ironically enough, Choshen Mishpat is one of the Arba'a Turim. Which brings another answer: the number of sections in the Arba'a Turim and Shulchan Aruch.
4 shades of white that constitute tzara'at. (Snow, plaster, eggshell and wool)
I know we all like to provide out-of-the-box answers, but I'm disappointed that I have to be the one to give this answer, and nearly two years after the question was asked - 4 Imahoth (Matriarchs).
We take 4 Minim on Succos: Lulav, Esrog, Hadas, Arava (Leviticus 23:40)
Four are the levels of the separative trop.
Four rivers emgered out of Gan Edhen "וְנָהָר יֹצֵא מֵעֵדֶן, לְהַשְׁקוֹת אֶת-הַגָּן; וּמִשָּׁם, יִפָּרֵד, וְהָיָה, לְאַרְבָּעָה רָאשִׁים"
Four kingdoms allied and won the first great war " אֵת כְּדָרְלָעֹמֶר מֶלֶךְ עֵילָם, וְתִדְעָל מֶלֶךְ גּוֹיִם, וְאַמְרָפֶל מֶלֶךְ שִׁנְעָר, וְאַרְיוֹךְ מֶלֶךְ אֶלָּסָר--אַרְבָּעָה מְלָכִים, אֶת-הַחֲמִשָּׁה."
Four corners require SiSith "גְּדִלִים, תַּעֲשֶׂה-לָּךְ, עַל-אַרְבַּע כַּנְפוֹת כְּסוּתְךָ, אֲשֶׁר תְּכַסֶּה-בָּהּ"
There are four types of death by a Beis Din - Stoning, Burning, Beheading and Strangulation. (Sanhedrin 49b)
They carried out the four death sentences against him (Bilaam). - Sanhedrin 106b
Pirkei Avos Ch. 5:
4 times when pestilence increases - 4th, 7th, and year after shemitta, and after sukkos (12)
4 types of people - what's mine is mine etc... (13)
4 types of mindsets - angers easily cools off easily, angers slowly cools off slowly, angers slowly cools off easily, angers easily cools off slowly (14)
4 types of students - Understand quickly and forgets quickly, understands with difficulty and forgets with difficulty, understands quickly and forgets with difficulty, understands with difficulty and forgets quickly (15)
4 types of tzeddaka givers - gives himself and wants others to give etc... (16)
4 types of people who go to the Beis Medrash - goes and doesn't study, studies and doesn't go, goes and studies, doesn't go and doesn't study (17)
4 types of people who sit before chachamim - sponge, funnel, strainer, sieve (18)
There are four shomerim - שומר חינם, שואל, נושא שכר, ושוכר. (Bava Metzia 93a)
Four are the fasts for the Mikdash.
(Hat-tip: my daughter)
Four is the number of cities King Nimrod sacrificed when he abandoned the cause of the Tower of Babel: Babel, Erech, Achad, and Kaleh.
Four is also the number of cities he was able to build as a reward once he got to Ashur: Ninveh, Rehoboth Ir, Kalah, and the great city, Resen.
(Gen 10:10-12, Targum Pseudo Jonathan ibid)