Caveat: My consistent feedback is that I use too much counter, and contemporary thinking about high level technique is that less counter is used today than in the bad old days of straighter skis, because (1) with more extreme sidecuts, less counter is necessary to turn (no more throw the shoulder forward like Stein Erickson), and (2) at high level racing, the G-forces are supposedly withstood better with a straight outside leg and less counter. It's said to be a "stronger" position skeletally if you don't use counter. In general, the newer mantra is to "minimize excessive tip lead" by the inside ski, and (in racing) to concentrate on increasing the edge angle by getting the inside hip lower to the snow, bending the inside knee, and putting the inside hip and inside foot only far forward enough to accomodate this deep inside knee bend on the angle of the hill.
That said, I find on the hill that throwing some counter late into the turn (1) increases my edge angle, when coupled with knee angulation, (2) loads up my outside ski to get it to continue to decamber and carve, and (3) does so by creating a natural break at the hip comma shape that is easier muscularly than doing a side crunch. (Those of us who are not low-FIS point racers don't often ski fast enough to rely solely on inclination, so we need some angulation as well.) I do need to remember to pull my inside foot back at turn initiation and keep it back so my weight is forward enough to (A) decamber the shovel of the ski properly and (B, repeating the mantra) minimize excessive tip lead.
I find a little counter helps me carve better, tighter turns. If they saw stills or videos, others on this forum would probably tell you (and accurately so) that if I reduced my dependence on counter and instead figured out how to get my inside hip lower and my inside knee more bent, I'd ski even better.
When to use counter:
1. Turning in a tuck. Along with knee angulation, it's one of your tools that still work in that bullet position. For some reason, knee angulation and counter work intuitively together for me in a high or low tuck. For an example, look at the cover of Lisa Feinberg Densmore's book Ski Faster.
2. In racing, for clearing a gate at speed, when you want a more aerodynamic impact, with less drag. If you saw the OLN coverage of Bode Miller's winning run at the Breckenridge downhill this year, there was a lot of that when he brushed the panels--Bode's line was closer to the gates than any of the other skiers, and to minimize drag and keep from getting spun, he put his inside shoulder forward at gate clear when he was close to the panel, so he just brushed the gate instead of hitting it square. With Bode, that gate clear counter is way up in the chest, not just hips.
3. If your form problems are the opposite of counter: Intermediate skiers often have their upper bodies following their ski tips (outside hand, shoulder and hip forward--ugly, and the enemy of carving). And hack slalom racers' standard problem (cough--guilty!) is reaching for the pole with the outside hand, which creates the same skid.
When not to use counter:
1. In slalom or for similar short radius turns. In my experience, excessive counter is slow and delays a quick release into the new turn.
2. If you find you have excessive inside tip lead