A thick southern accent is far easier for Americans to understand than a thick foreign accent. I've never heard a native English speaker that I had a hard time understanding.
A couple of years back, I met my friend's grandma down in the bayou on the border between Texas and Louisiana. I had absolutely no clue what that woman was saying to me. I had to look at my friend for a translation every time she spoke. He assured me that she was speaking English.
Plenty of Singaporeans or Indians are, in fact, native speakers with accent and dialect differences that can stymie other English speakers. I've had people complain New Zealanders speak too quickly for foreigners to understand (as well as our flattened vowels). And get back to me after watching Taggert.
(The most incomprehensible language I've ever heard from a native speaker personally wasn't Glasgwegian, but rather two 60+ folks demonstrating Black Country English.)
I would say that depends on the southern accent in question. I (native english, mid-east coast) have never had trouble with Texan accents at all, no matter how strong, but have had a lot of difficulty with rural accents from people in South Carolina. A few weeks ago I was down there visiting and tried to buy some shrimp from a native South Carolinian. I had to resort to hand-gestures; he seemed to have as much difficulty understanding me as I did him.
My wife's family comes from the coastal islands off South Carolina.
They speak English, but I just could not understand anything the locals said. The dialect/culture is called Gullah: http://en.wikipedia.org/wiki/Gullah
Listen to some "native English speakers" in Glasgow - I understood them reasonably well after a week, but when I arrived the cab driver might as well have spoken chinese, I had to write things on paper to get where I wanted...
I am Indian, but a native English speaker. When I went to Northern Ireland, I took a long cab drive to meet a customer. For the first 15 minutes of that drive, the driver and I were trying to calibrate accents. I certainly couldn't understand a word he said. After a while, things magically started making sense.
I occasionally have—some Newfoundlanders, people from certain parts of the UK, and so on. There's a whole lot of variation in the English-speaking world, and the line between dialect and accent isn't well-defined. There's even an island off the coast of Virginia (I think) where people speak 18th-century English!
I don't know what island you're referring to, but there are a lot of claims out there like this - a lot of people claiming they speak the "Queen's English". Every claim I've heard, much like Eskimos and snow, turns out to be a myth:
The "18th century" thing stuck in my mind from some media piece, and now that you mention it, does sound rather obviously like a myth. But the place exists—I think it was probably Tangier Island [1], and the accent there is indeed archaic:
Some of that sounds like a Monty Python sketch! It's definitely an example of one native English speaker (me) finding another (them) hard to understand.
I also second the commenter who brought up the Glaswegian accent. I love how it sounds but damned if I can make out half of what they're saying.
