The Hartford Convention during the War of 1812 involvd New England States such as Connecticut, Rhode Island and Massachusetts, in which they discussed what could and should be done about the limits placed on merchants by the war in terms of who they could and could not trade with. They were particularly mad because their business had been ruined almost continually since the Revolution. French and British raiders, pirates, the Embargo Act, the Non-Intercourse Act and now the War of 1812 had made it almost impossible to profit as a merchant. That being said, secession was not a serious part of the Hartford Convention, and it was not even brought to a vote. What's significant is the fact that it was mentioned at all.
South Carolina is the birthplace of true secession, with newspaper editors like Edmund Ruffin arguing for decades before the Civil War to break away. Georgia would come in close second place in my book, always suspicious of the North and convinced the southern states would be better off on their own.
This depends on what time frame you're talking about.
Serious talk of secession goes as far back as the War of 1812. Towards the end of that war, New England states met in what was known as the Hartford Convention to discuss seceding because of US involvement in this war. They thought it hurt them more than any other part of the US and benefitted them less.
The next time secession came up, it was South Carolina that led the way. This came about because of the "Tariff of Abominations" of 1828. The South felt that the tariff hurt them (because they depended on imports and exports) and helped the North (because they were much more self-contianed economically) and argued that they might as well secede if such laws could be passed.
At the time of the Civil War, South Carolina was, once again, first to go after Lincoln's election convinced them (and other states) that the South would be ignored (at best) by his government.