As I learned recently, there is actually a good reason why gcd(a, b) is often abbreviated as (a, b). Roughly speaking, in ring theory, an ideal I is some subset of a ring (which you can think of as a number system, sorta) for which ai is in I (if a is any element of the ring and i is in I). Given any element x, we can generate an ideal from x by just taking every other y in the ring and computing yx - if every yx is in the ideal, then multiplying by some other z to get zyx is the same as just having (zy)x ,which is just a different multiple of x. This ideal - the ideal generated by x - is written as (x); if it's generated by multiple elements, it's written as (x1, x2, ...).

If you consider the ring of the integers, then the ideals are multiples of some integer. For instance, the multiples of three are an ideal, because multiplying a multiple of three by any integer yields a multiple of three (so if you multiply the set of multiples of three by any integer, you just get back something that's in the ideal).

The final point is this: the ideal generated by two integers is actually just the set of multiples of their gcd. Therefore, if a and b are integers, (a, b) is the set of multiples of their gcd - just like (3) is the set of multiples of three. This is why the gcd is often written in this way.

The cool thing is that this works in rings in general, not just integers. You can extend the concepts of gcd, primality, divisibility, etc to rings in general, and operate on things besides just integers, such as matrices, polynomials, or rotations of a cube.

For more info:

  http://en.wikipedia.org/wiki/Ring_theory
  http://en.wikipedia.org/wiki/Ideal_(ring_theory)