Waiting for four months is ordained for those who take an oath for abstention from their wives. The waiting period of the woman whose husband dies is four months and ten days. When Abraham said: "My Lord, show me how You give life to the dead," Allah said: "Why! Do you have no faith?" Abraham replied: "Yes, but in order that my heart be at rest." He said: "Then take four birds, and tame them to yourself, then put a part of them on every hill, and summon them; they will come to you flying. [Al-Baqara 2:260]
The respite of four months was granted to give time to the mushriks in Surah At-Tawba so that they should consider their position carefully and decide whether to make preparation for war or to emigrate from the country or to accept Islam. Those who accuse honorable women (of unchastity) but do not produce four witnesses, flog them with eighty lashes, and do not admit their testimony ever after. They are indeed transgressors. [An-Noor 24:4]

Taoism
Four Symbols of I Ching

Other
In a more general sense, numerous mythological and cosmogonical systems consider Four corners of the world as essentially corresponding to the four points of the compass. Four is the sacred number of the Zia, an indigenous tribe located in the U.S. state of New Mexico. The Chinese, the Koreans, and the Japanese are superstitious about the number four because it is a homonym for "death" in their languages. In Slavic mythology, the god Svetovid has four heads.
Four-dimensional space is the highest-dimensional space featuring more than three regular convex figures: 

Two-dimensional: infinitely many regular polygons. Three-dimensional: five regular polyhedra; the five Platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Four-dimensional: six regular polychora; the 5-cell, 8-cell or tesseract, 16-cell, 24-cell, 120-cell, and 600-cell. The 24-cell, made of regular octahedra, has no analogue in any other dimension; it is self-dual, with its 24-cell honeycomb dual to the 16-cell honeycomb.