I see a lot of long answers up there, and no offense to any of you; they are all good! I just like to keep things in grade-two mentality and get to the point fast. I suggest changing everything every four to six weeks. If you go any longer than six weeks, your body will adapt and further progress will be minimal. Not to mention, boredom will set in and relapse might occur.
If adherence is a problem, changing exercises can help, otherwise there are no fitness-related benefits.
The idea that we can be too well adapted to an exercise to obtain a benefit is simply unsupported by any evidence. Muscles become stronger, for example, when they adapt to a higher level of resistance, not when they adapt to a new exercise. Repetitive-use injuries are better addressed by maximizing the efficiency of your workouts or by adjusting your workout schedule.
Here’s a simple example: Let’s say you want to improve your upper-body strength. How would you measure it? Most people think that the bench-press is a good indicator. As far I know, there’s no evidence that doing anything else other than progressive resistance training with the bench-press itself will maximize your performance. (You might get some benefit from training individual muscles, but the improvement will come from increasing resistance, not from adaptation to a new movement.)
So, I guess my answer to your question is either “never” or “as often as you like”. 😉