The answer may surprise you.
In answering this question, the first instinct is to answer “when you first start an exercise routine.” There is a lot of truth to this statement.  This is your chance to develop great movement patterns and to create habits that you can build on going forward.

I personally spend  A LOT of time un-programming bad movement patterns out of clients that have been lifting with terrible technique since high school.  This takes time and will inhibit the progression that a client could make should these patterns not exist.
Even when employing these sub-par techniques, a first time lifter will realize strength gains and will generally progress despite a well thought out program utilizing proper technique.  The brand new stimulus will force an adaptation even if the exercise is performed less than perfectly.  This is not ideal, of course, and bad habits will develop and possible injury may occur.  The fact is, the novice lifter will see results at first even with a shoddy program.
As an athlete or fitness enthusiast progresses from novice, to an intermediate level, and then to advanced, the subtleties of the training program become VERY IMPORTANT to ensure continued results.  Once the initial shock and adaptation of the beginning months of training disipates, program design becomes more important.  As a matter of fact, a very advanced athlete nearing his or her genetic potential must program there workouts with a precision that allows them the smallest gains.  Small gains can make a BIG difference over time.  The difference between a 4.4 40 yard dash and a 4.5 (although only 1/10 of one second) can mean the difference in scholarship money and record setting performances.  Even with a recreational fitness enthusiast, these small gains are important.  Let’s face it, when you work hard it’s important to see the fruits of your labor. Hardly anyone I know works hard just to spin there wheels in place.
In short, having a professional guide you at the beginning of your fitness routine is important.  However, as far as results and continued change goes, an exerciser or athlete at an ADVANCED level simply must have a precisely designed program.  The smallest fine tuning matters more at this stage of a training career than it did at the beginning when ANY stimulus would force a change.
Matt Pirtle, MA, CSCS