I think it depends on several factors:
First, your holding time. If you're targeting two point in the ES and you expect to get there in a few minutes, most of the time things in the market aren't going to change that much (and if they do, your 1-2 point stop will be hit before you know it), so for most people it makes sense to let your orders be.
If, however, your holding time is longer (I'm not so much talking about timeframe but number of bars) things can and do change. Some people think that leaving your original orders in place and sticking to your guns when things change shows discipline; without meaning to offend anyone (that comes later

) I think they confuse discipline with stubbornness: if the reasons for the trade have changed, so should your management, you just have to determine a way to be able to tell that it's the market that has changed, not your emotional state.
Second, your trading style. If you're fading extremes, catching counter-trend swings, doing mean reversion, etc., it makes very good sense to move your stop to breakeven because, based on your view of the market price should not go back to your entry price once it's moved a certain amount in your favor. That is, if you get stopped out at b/e, your assessment of the market was wrong (or early, as you wish), regardless of what happens next.
If, on the other hand, you're following the trend - and you're entering in logical places, i.e S/R, etc. - retests are normal and even though moving your stop to b/e will spare you the occasional loss, it will also kick you out of many good trades, usually without giving you the time/opportunity to reenter at a good price (for a leg of the trade anyway - it always marvels me how some people will tell you that if they hadn't been stopped out by one tick three months ago, now they'd have a huge trade).
Note: the best thing you can do is run a backtest in your computer (or by hand if you take few trades) and see how your results would have been if you had stuck to one or the other system (or a selective use of moving your stops/targets based on some reasonable logic, not on over-fitting). NinjaTrader (if I recommend it to one more person, I'm gonna start asking for money

) has a feature in its DOM by which you can select a "Shadow" strategy and see in real time how much you'd be making moving or not moving (see picture).
Third, your "technical" level of experience/skill and emotional self-control. The greener you are, the less you should fiddle with your orders because a) you'll have a hard time distinguishing between noise and signal and b) you'll be swayed by your emotions.
Finally, I'd say that great traders (with the exception of those using automated systems - and even them have contingency plans to make exceptions) DO change their stops and targets, only that they don't do it without rhyme or reason, but as conditions warrant.
PS: I know Schizo's secret - but I'm not telling - or maybe I am
