I teach in a club that has a rule that "touch and goes are not allowed." If a student wants to practice take-offs and landings, the rule is to make the landings in a "stop and go" fashion.
As far as the instructor is concerned, I think this is a good idea - especially in the beginning of teaching a student to land. It will allow the student to develop their technique for cleaning up the airplane for a proper take off and give the instructor time to verify everything.
The clincher was when I heard that touch and goes are actually bad for the airplane and engine. I am not sure why this would be, but am going to try to figure it out. It seems to me that if a student (or even an experienced pilot for that matter) would like to practice take offs and landings, that a touch and go would provide better engine cooling and less wear on the brakes. It would also provide the student with forward speed that would allow a quicker take off. (A stop and go would require more runway). One might even argue that the touch and go forces the student to divide attention inside and outside of the aircraft - A skill you are trying to teach anyway.
Alternatively, it also introduces risk. Doing a clean up on the aircraft while still in motion takes some level of skill. If there is a cross wind, that just ups the ante.