Sure, but it requires you to change module's class names and in code references.
For instance if you would like to create a clone of tasks module, then you should copy directory to e.g. Custom/Tasks, then rename every CRM_Tasks to Custom_Tasks. If you'll change Tasks to TasksClone, then you'll have to change files names and class names... To get better understanding please review sections about module development on our wiki.
Regards,
Adam
PS. To do some little changes it would be better to create "Extending module", that will change some fields, add new, etc, instead of cloning whole module.