Certain national fellowships (Fulbright and others) require letters from an archive describing the scope of their collections and the relevance of these collections to your research project. For one example, see the preparing for an archives visit on the course wiki.
Letters of Introduction: Many French archives require formal letters, called attestations. These letters (in French) cover the student's level, enrollment and project and their advisor's title as someone who is authorized to direct doctoral research. These letters typically come from the graduate advisor or director of graduate studies. Facutly doing research, often get letters from the dean of the college. Researchers should also be prepared for an introductory interview in French.
Other Documents: Passports and passport photos are required (although many institutions now use digital photographs taken on site) in order to obtain a library card.
Letters of Introduction: Letters of introduction should be written by student's supervisor or the department chair. Good letters verify a student's credentials: BA and/or MA in X discipline; currently enrolled in PhD program; working on XX topic for dissertation; dates the student will be abroad; perhaps any special language skills the student has.
Other Documents: Always bring extra passport photos to attach to a reader's card, if necessary; the letter of intro; and the passport. Most places now will take a digital photo but it helps to come prepared.
Other tips: In Italy requirements for working with archives and rare book or library collections can differ. In many cases, letters can be in English or Italian.