The answer to this question is virtually never.
It's possible I'll get a comment or two listing successful books with prologues, but it doesn't matter. Agents tend not to like prologues, and that's putting it mildly. Sometimes you can bend the rules and make it work, but generally it's better not to when you're trying to break into the challenging world of publishing. In Les Edgerton's book Hooked, which I've been reading this week, he mentioned that prologues are usually unecessary backstory dumps. Ninety-nine percent of the time, you're better off incorporating it into the rest of the book instead.
Of course, I had stuck a prologue on the front end of my middle-grade sci-fi book. If prologues don't show up in adult fiction much, they really don't show up in middle grade. It wasn't really an information dump, since I didn't give the reader much information in it at all. It was just a chunk of action that I hoped would catch the attention of the reader. It helped me get my story moving and define what direction I wanted to pursue. My writing group liked it there, but I'm planning to can it because I believe I'll be able to release that information throughout the story instead.
So back to the original question. Is there any time when a prologue is okay? I think the answer to this is yes. When you're knocking out that first draft, a prologue can be helpful to you as a writer in helping you set the stage for your story. First drafts don't matter that much anyway, primarily because most of them get thrown out or changed. An example is Richard Peck, who writes his first draft and then throws away his first chapter and writes a new one. In the first draft, you're telling yourself the story. In later drafts, you're telling your reader the story. You might need that prologue when you're telling it to yourself the first time, but don't get too attached to it or feel bad if it isn't good enough to make the cut of the rule-breakers. Better to publish with no prologue than to hold onto something that's a death knell to your publication chances.
One more thing. Before you decide there's no way you'll part with your prologue, read Hooked, because if you can't hook a reader (and remember the first readers will be discerning agents or editors with sensitive literary tastes), your book is dead in the water.
For extra info on what's happening in children's literature, stop by my Examiner.com page for book reviews and interviews with children's authors and illustrators.