I realize it may depend on what you're doing, but as a general rule, which is preferred and why?
Alton Brown talked about this on an episode of Good Eats, and here's what I remember:
If you cut with the grain, you'll end up with long strands of protein, like this:
From what I understand, this means that it'll be pretty chewy. Your mouth has to work harder to break the strands up into smaller pieces to be more easily swallowed.
If you cut against the grain, you get strands like this:
You can see that the strands are much shorter, which means the meat will fall apart more easily (each strand doesn't have as much surface area to connect to adjacent strands) and will therefore be more tender.
I almost always cut against the grain, as it tends to make the meat softer when cooked. Also, since cutting against the grain can be difficult to do without shredding, I partly freeze the chicken first by leaving it in the freezer for a half hour - much easier to slice that way.
One exception is if it's going into a stir fry. Then, I tend to cut along the grain, because really thin slices cut against the grain have a way of falling apart in the wok (at least, they do for me).