Definitely on balance you see more 2*pi in equations than pi alone, but 4*pi, pi/2, and pi/4 are also quite common. If I were stranded on a desert island with nothing but a pencil and an endless stack of paper and decided to rederive all mathematics and physics I would probably use 2*pi as my basic trigonometric transcendental number, but I think the people who get worked up over this (several of my friends included) are crazy nutbars who will get excited about anything.
Of course, I tend to think of 'getting the factors of 2*pi right' is a job you leave to engineers once the physicists are done, so probably you should take my opinion with a grain of salt.