6 is equal to the sum of its proper divisors: 1 + 2 + 3 = 6. This makes it a perfect number, and in fact the smallest number with that property, with the next being 28.
6 is equal to the sum of its unitary proper divisors, that is to say divisors d such that d and n/d are relatively prime. These are called unitary perfect numbers. It is the smallest number with this property.
Six is the basis of Robert Munafo's idea of classes. 6 is the boundary between class 0 and class 1 numbers, 106 is the boundary between class 1 and class 2 numbers, 10106 is the boundary between class 2 and class 3 numbers, and so on.