Over what was the Civil War fought?

Excellent answer!  Of course, as Edward A. Pollard pointed out in A Southern History of the War (published 1866) the primary reason was economic exploitation of the South by Northern industrialists and the Federal government, largely centering on tariffs.  Eighty percent of the income of the United States government came from export duties on agricultural products from the South.  But import tariffs were extremely high, as a means of economic protectionism for industries in the North.  This meant that, although superior products were available from Europe and were much less expensive than products from the North, after the import duties the prices were so high Southerners were virtually forced to buy tools and other products from the North.  This simmered for decades, and the war almost broke out several times before the 1860s just from this issue.  The protectionist idea was probably a good one in the 1790s, but by the 1840s was a serious drain on the Southern states' economies, and no longer necessary to protect industries in the North.

The States' Rights controversy was also a major issue, as the Federal government took more and more power to itself not specifically given to it by the Constitution.  Although all such powers were guaranteed to the states by that document, the Federal government began accumulating further powers within the first few years of the new republic, a process which has continued to this day.

Slavery became an issue principally because of the troubles in Kansas and Missouri, caused basically by bandits claiming their actions were inspired by pro- and anti-slavery principles.  But the triggering incident of secession was the election of Abraham Lincoln as president.  Although the facts have become obscured, it seems some of the Electors (who are of course appointed, not elected) changed their votes from the way their states voted, and appointed Lincoln president.  Since proceedings of the Electoral College were very difficult to find anything out about, whether true or not this was the deciding factor for South Carolina's secession.

Lincoln's position was that while the people had the right to rebel against the government if they felt that government to be oppressive, the states did not have the right to leave the union. I believe he was right, and that had the Confederacy remained North America would have become a land of several smaller countries, all continually at war(much like the Europe the American people had escaped from).  As far as I've ever been able to determine it seems the South was right about everything but slavery, the moral issue.  And, as Napolean said, "The moral is to the physical in war as three to one," and being morally in the wrong was as bad a disadvantage as the population and industrial might of the North.