There's no rhyme or reason to it, really. You can book eight months in advance and not have anything change, or you can book one month in advance and have a change. Here in St. Louis changes have been pretty common since American cut their daily flights in half on Nov. 1 and they've been tweaking the schedule constantly since then. If you're in a more stable market, your risk of getting a change might be smaller.
Usually the impact is relatively minor; an hour or less one way or the other. However, if the change will cause you to miss a connection or the flight is cancelled, the airline should be willing to accomodate any reasonable request. Of course, that assumes that there are any other viable options. Your chances of getting a free change are best if you have another option on the original airline. If the change you want requires switching to another airline, you may have more trouble.