This is an interesting thread (I actually like what-if's. Maybe that's why I like Civ so much... but I'm not a history buff). I suppose the first question would be, "How did the South win?". Suppose some battles turned the other way (i.e., the famous pickett fence for one. Suppose the landowner happened to take it down for some reason, and the Confederates had a much easier time). True, you could say that the north was more industrialized, but let's suppose certain circumstances happened. Also, I've read that European nations had very much a lot at stake with the US civil war (ironically, I think, since the next 100 years would prove that). Let's say that England was able to advance slightly more with their Industrialization, and convinced the south that some industrialization was good, if not temporary.
Now, supposing the South had won, what would've happened? I think that first, certain things wouldn't happen, like the Alaskan purchase (no one suspected it had oil then). The fact that Russia owned this piece of land would place a Soviet foothold on NA in 1917. Now, back to 1866. I'm pretty sure several things would've happened. First, the South might've demanded that the north give up their territories to the British, which would've been their allies. This is where I mostly agree with Marla's map. I don't agree that the California lands would've been that great. I also think that America, beaten back badly, would've been forced to give the central land to the Native Americans (Probably mostly Sioux). The rest of the land would be taken by Canada, giving England a major presence in the north. Spain wasn't in a posistion to retake land (they were selling it). Russia wouldn't have had any one to sell land too, since most in Europe would be too far away. California would be seen as a "US Gold Colony", and any trade/commerce from that region would've been expensive. I doubt that England, the Confederates, Indian Nations, and possible Mexico would have let trade travel through their lands. Atleast not with all of that wealth. It would have become a power vacuum. I also think that the capital would have been moved from Washington DC (and away from the coast). Maybe somewhere in Ohio, or Chicago.
Now, since America is down for the count, there's several
very important things that don't happen.
Causes:
1 - US Doesn't purchase Alaska, which most likely stays in Russian hands.
2 - US doesn't arrive in Japan, opening doors to trade.
Effects:
1 - Russia has a foothold in North America come the Soviet Revolution.
2 - Japan doesn't rise to power in WWII.
Shift to 1914. America is still becoming industrialized, but isn't a major power it would have been. The south would still be a primarily agricultural society, slowly giving into industrialization. The south, I think, would be poor, like others said. The north wouldn't have the breadbasket of the south to sustain its' production and workforce. Europe would still be in a world war. To the best of my knowledge, the US was pretty much isolationist until 1917. Germany probably would have still lost the war. WWII still would have happened, probably with more dire consequences for Europe (especially England), since the US wouldn't be able to send as many troops. It's lessened size would mean less numbers. The Soviet Union would still be flourishing, and China would still become communist (according to
this site, China was already on the road to becoming Communist). China, or Russia would have invaded Japan, Korea, and the rest of Southeast Asia. Germany probably would have achieved one of its' goals to reproduce or emulate the Roman Empire. Russia probably would have invanded the Middle East too, attempting to both stop Germany from expanding to their south, and getting a southern port, with Iran and Afghanistan being a major source of resistance for the Russians.
I'm not sure what if India would've been able to hold out, or if it would've still been a British colony (probably not). Russia and China would have been strong allies, with a blood feud against Germany.
Which brings an interesting question. Would the Atomic Bomb have been developed around then? If so, what next? Also, the Soviet Union would have had a foothold in North America (if they haven't sold it to the British. Would the Russians and Germans have been more willing to engage in nuclear warfare?
In short, I think there would've been
major world repricusions, affecting both World Wars.
I like detailed what if's myself. By the way, I live in the only state to secede from another, West Virginia 
