A major issue with the use of company e-mail is that they invariably specify, usually in the employee handbook, that you have no right to privacy in company e-mail. They often have filters to block adult sites, on-line gambling and the like - it is simple to also put in filters to look for words like resume and such. I cannot put it more succinctly than
DO NOT USE COMPANY RESOURCES FOR YOUR JOB SEARCH!In this day and age, everyone has a personal e-mail - use it. However, make certain that your address is professional -
redhotlover@whatever.com or
hotpartygirl@whatever.com don't cut it. (In fact, I once rejected an applicant for having a similar e-mail - gave me serious concerns about his judgement.) Get a free g-mail address for your job search if you must, and have it say something like
yourname@gmail.com. In the increasingly rare case that a fax is needed, go to the local copy shop and send/receive it from there.
Parker is correct that academics think nothing about using their institutional e-mail for things like this, and there seems to be no problem with this. However, even in the academic setting, I think that it is preferable to use your personal e-mail. That way, there can be no question of misappropriation of resources.
Hope this is useful.
Dick