A resume should never be stapled together. If something must be used to hold it together a paper clip may be used but even this is not recommended.
The reason that stapling is strictly forbidden as a practice when sending out a resume is that many companies use applicant tracking software which requires that they either scan or feed the resume into a machine to copy it to their database. When a resume is stapled it creates and extra step for the recruiting office and may very well cause the resume to be thrown away rather than considered. A resume should also not be folded since this will also interfere with the scanning process.