I've read a few books that do this well. The Redwall books, and Harry Potter. But these authors did it subtly and they didn't do it all the time with every character that had an accent. Jim Butcher, however, hasn't done that, and I haven't had ANY trouble imagining how his characters speak.
This came up because in the book I'm reading right now, the characters who speak "country" English (for this setting) do so in a way that feels unnatural. I've heard people speak the way she's tried to make them speak, and it just doesn't sound right. The reason, I believe, is that she does this with nearly every sentence of dialogue from these characters. It's not awful, but it is distracting. It pulls me so far out of the story that I can only read a few pages at a time before I have to put the book away.
That's also the reason I pulled all of the accents out of my story. When I read through the book on my first editing run, I realized RIGHT AWAY that it didn't sound natural, especially when I read it out loud.
My advice for anyone who wants accents in their writing: read it out loud, have someone else read it out loud, and make sure that you don't overdo it. A little bit will go a long way when you spell out the accent. And if it you don't want to spell everything phonetically, just do what Butcher (and many other successful authors) does: tell the writer that the character's