I love E-Mail. E-Mail doesn't interrupt, it quietly sits there until you have time for it. E-Mail allows you to carefully think about what you want to say, and edit it if you change your mind. E-Mail is permanent, so you can look up what you were asked and what you replied and if necessary you can even prove it.
Yet there are times when you definetly must use a phone (or if possible just walk over to that office):
If you are getting angry use the phone (Not because more satisfactory to shout on the phone) . On the phone you will heare the nuances in the voice and in general get way more information across the wire. Chances are the insult in the last E-Mail was just unlucky wording, and the problem is solved soon, once people start talking to each other.
If the recipient is busy and doesn't know about the importance of your request. It is a little mean to interrupt someone who is busy, but sometime you don't have a choice. If you get 50 or 100 E-Mails a day sooner or later you will start filtering really aggressively. And even if an E-Mail isn'tÂ actively categorized as 'not that important' might just happen it slips through. And the sender will never know. He just won't get an answer.
It is hard to ignore somebody on the phone. And even harder to ignore him without him noticing. So if you need to get stuff done by somebody pick up the phone and tell them. Just for the record you might add a confirmation mail afterwards.