Unintelligable English

I remember ages ago there was a post of I think it was a Welsh girl supposedly speaking English that was incredibly difficult to understand. I'm wondering about this general topic because in my Spanish class we read an article where someone from the RAE stated that they wanted to maintain proper Spanish in such a way that "cada hispanohablante sea capaz de entenderse con otro, algo que no ocurre con el inglés." My first thought was that this was bull, because while I've certainly ran into for example thick Scottish accents where I had to listen rather carefully to understand, I've never heard a native English speaker I just plain couldn't understand. Can anyone relate any experiences of not being able to understand some accent of native English, or better yet provide some recordings?

And while I'm interested in thoughts from non-native English speakers too, if you post could you please qualify that, for obvious reasons?