I am interested in any development of moodle that would allow the sharing of
activities between courses.
First of all, just a quick note about terminology. Joao wrote, "How can a module "belong" to more than one course?", I think you mean, how can 'activities' belong to more than course. Modules are the things that you use to make activities. Anyway, I see two possible versions of a 'sharing of activities' feature:
1) Activities could be copied into other courses. At the moment this is possible via the backup and restore feature. However, it would make things much easier if it were possible for a teacher to, for example, click on 'Quiz' in the 'Add an activity ...' menu, and then be faced with a list existing quizzes, one of which could be chosen, and thereby copied into the course as a completely new quiz. With this version of the 'sharing of activities' feature, the copied activity would become a completely new activity, independent from the original. So in the case of Quizzes, the results would be completely separate.
2) The second version of the 'sharing of activities' feature would be just that - sharing. A teacher would in effect be creating a link to an activity that existed in another course. By making this link, students would automatically be given access rights to that activity, but not to any other activities in the originating course. Using the example of a Quiz, a teacher would click on 'Quiz' in the 'Add an activity ...' menu, and then be faced with a list existing quizzes, one of which could be chosen. Unlike the above scenario, instead of copying the quiz to make a new one, this selection process would in fact be creating a link to the original quiz. Thus, the results and other data would not be separate, they'd be stored on the original results
database set up for the original quiz.
I imagine that from a programming point of view, option 1 would be much easier to set up. Option 2 would be wonderful, but I'm sure is rather complicated, and potentially contains a number of problems as mentioned by Tim (see above).