Often this works, but sometimes you'll hit a library that simply doesn't have the staff to make ILL to outside libraries a priority. But wait, perhaps your journal is available online somewhere, but you don't know where. Another useful reference book to have on hand is Bibliodata's Fulltext Sources Online. As an added bonus, subscribers to Fulltext Sources Online also get access to Bibliodata's Internet list of full-text sources available on the web. I fax a list of articles I need, they check their holdings, and fax back the articles that they have available.
Commercial services are often excellent choices.
If your item is chemistry related, you can call Chemical Abstracts. I recently used them to locate a very esoteric Japanese technical journal. But while they have a great selection, their collection doesn't go back farther than 10 years. They're fast, cheap and good. They use the engineering collection at the University of Minnesota.