Six

... is the sum of the first three positive integers.
... is the third triangular number.
... is three factorial (3!), the product of the first three positive integers.
... is the first perfect number. A perfect number is equal to the sum of all positive divisors smaller than itself.
... is the number of sides of a hexagon. The hexagon tiles the plane.
... is the number of faces of a cube (hexahedron). The cube tiles space.

From the television series The Prisoner:

"Who is Number One?"
"You are Number Six." (hint: "You are, Number Six.")