I heard about a study project where a student took 100 of the 'best' images she could find, and overlaid the 3rds grid. Something like 80-90% of them did closely adhere to the 'Rule of Thirds'....is I'd say it's a successful method to use. However, when I hear "largest and most repetitive critique at the competition I entered a few of my photos in was rule of thirds"...I tend to think that the Judges were either lazy or incompetent. Just saying "you should have used the rule of thirds", isn't much of a critique in my opinion...but it's easy to say and makes you sound smart. :roll:
Of course, one of the worst enemies of good/creative composition, is the habit of keeping your subject in the centre of the photo. I'll admit that I sometimes fall into this habit and forget to recompose my shots after focusing using the middle AF point. So when giving a critique, and the subjects are mostly centered....the most basic suggestion is to use the rule of thirds.
Another tip I read (aimed at point & shooters) is to take a piece of sticky pad and cut out a small square, then stick that in the middle of your LCD screen. Then compose your shots so that you can see your subject (around the edges of the sticker).