Applicants need reference letters and ask suitable more experienced people who have firsthand knowledge of their abilities, to write about them. I am available to write letters for students, postdocs and professors who have worked with me, both recently and in the past. However, as I am asked by about 40 people every year for letters this is a considerable amount of work for me if I am to do a good job (typically a letter for an undergrad takes about one hour, for a new PhD about two to three hours, and for an experienced professor anything from four hours to two days depending on how well I know their work beforehand). This means that, if all goes well, I work for 120 hours a year on reference letters, for which I do not get paid or directly rewarded. I do not mind using my time to help people but it makes my job much easier if the applicant provides me, in one email, all of the information that I need to write the letter, and sends me the information well in advance (three weeks or more) of any deadline (I may be too busy to write your letter in the one week before the deadline).

For an undergraduate student, applying for summer research projects, or for funding for graduate school from NSERC or FQRNT:
I need your CV/resume, your transcript (official list of grades), research plan (if you have one), details of where you wish me to submit your letter (and deadlines).
If you have taken a course from me: please tell me what class, when, and what your grade was.
For NSERC and FQRNT there are websites -- you must go to them and set up an account, include there all the information that they ask for before you ask me for a letter (when I input the reference letter, I want to do it that first time I go to the website, and that usually requires you to have done your part first).
Often for NSERC and FQRNT the first decision on funding is made in your department, so find out the address for reference letters there (and the deadline).

For graduate students and other applying for postdoctoral positions or first tenure-track job:
I need everything you will submit with your application. For example: research summary, research proposal, CV; almost finished drafts will do but I do not want to feel like I am the first to read them (ie get a colleague to read and edit them).
I need easy access to your (p)reprints (but if you have many, pick your best five) -- it is easiest if the pdf file can be downloaded, either from your webpage or the arxiv (in which case give links, I do not want to hunt for them). Absolutely no zip files or tex files.
No applicant needs more than four research letters; it certainly does not help your file and you are wasting the time of the letter-writers. Please do not ask me if you have already asked four people.
At MathJobs, I am Andrew Granville with email address: andrew@dms.umontreal.ca --- Please do not use any other variation.