When is it acceptable to ask a graduate program about their admissions decision?

If there's a specific reason, such as a deadline at another school, that it would be helpful to know your status, then I think its very reasonable to send a message to the graduate director at a program you're considering. Asking just because you're curious is generally discouraged, but if you have new information, then its reasonable to ask for an update.

I would say that in general it is OK to ask if you haven't heard from the program in a long time or if you, say, see decisions being posted on The Grad Cafe. Sure, you don't want to be e-mailing them every week, but a short e-mail to the graduate department (not necessarily the graduate director, but the person listed under who to contact for graduate admissions) shouldn't hurt and they shouldn't be offended or annoyed by it. If they are getting swamped by such e-mails, it is not hard for them to just ignore them and not reply. If they only get a couple, however, they might actually give you a better estimate of the timeline.

Personally, I also consider answering e-mails asking such questions to be a part of the job description of whoever is the contact person for graduate admissions. Yes, the graduate director should not deal with such questions, but that is why I also think the graduate director shouldn't be listed as the contact person.

To sum it up, I only think it's "inappropriate" to constantly bugger them, but not to send a polite e-mail asking about your status.