I just "coffee'd" my plants after reading this. I hadn't done so in a long time. Typically, it's something I do once a year or so, while relying on fertilizer every two months or thereabouts (it used to be every two weeks, but I get lazier the longer I grow these things).
In the past, I've been part of this debate, using plant physiology jargon as well as firsthand experience to make my case. However, the topic has acquired the scent of a bloated, decaying horse (for me, anyway). That being said, David (Big Bella) has eloquently summed up why many of us use coffee in as concise a description as I could imagine, and he has done so in numerous posts over the years. Regarding my experience with this form of supplemental nutrients, I do notice improved growth in certain plants, whether some species simply metabolize these compounds more effectively, appreciate the acidity, or perhaps are benefiting because of the media they're in - I'm not entirely sure. I have noticed that species found naturally in serpentine soils benefit conspicuously more from this than others, but again, I'm not sure why, and perhaps the results won't be the same for others who follow suit.
As a note for new growers who are curious about trying this nutrient regimen, I will say that it doesn't harm the plants, which is something that can occur when inexperienced growers decide to "experiment" with synthetic fertilizers. But as with any nutrients introduced into a contained substrate, flushing is always recommended to improve airflow and reduce growth of unwelcome guests. This applies to both coffee and synthetic fertilizers.
I'll probably continue to use both synthetic fertilizer (Grow More urea-free or Maxsea all purpose) and coffee for the foreseeable future, but I don't put too much stock into it these days. There are factors in the environment that I have more trouble maintaining than nutrients, such as temperature, root space, light, humidity, pests, etc.. All of which have profound effects on the health and growth rate of these plants. It's often recommended that you should only supplement nutrients once your plants are already healthy, as you will be able to gauge how much, or how little, is needed (as Butch (Av8tor) touched upon above). In addition, these application rates further depend on factors such as temperature, light, media, moisture,, CO2 availability, etc., which are all limiting factors in almost the same way nutrients are limiting factors.
A pretty good rule of thumb for those "new" growers reading this now or years from now: Make sure your thumb is green before you purport to have one.