I can't speak for other interns, but I was never asked to do things like make or buy coffee. One of my managers said to me on the first day, "You're here to learn, so if there's down time, then don't be shy to ask us for something to do." The other manager said he remembered having to get coffee daily for the executives when he was an intern and he vowed not to do that to interns in the future if he was ever lucky enough to be in a position to have interns.
I've never been in favor of sending interns to get coffee, and an informal poll of a few colleagues and friends tells me that I'm not totally crazy for taking this stand. And I'm sure I'll ruffle the feathers of people who think that being sent on coffee runs is part of "paying your dues," but I don't think we should make people do the things we hated doing just because we were treated that way too. I reject the idea that "everyone's had to do it in their internship" is a valid reason to send an underpaid (or, in some cases, unpaid) student or new graduate for a Starbucks run. There are free coffee machines in the kitchen for a reason--quality, be damned. You can get your chai latte later yourself.