I would identify the Union victory at Vicksburg on July 4, 1863, as the most important military turning point of the war.
The fact that this occurred only a day after the victory at Gettysburg is significant. Though Gettysburg is more prominent in the popular historical consciousness, Vicksburg was probably more significant militarily because it meant that the Union now controlled the Mississippi river, in effect severing the western part of the Confederacy from the east and preventing the South from using the river as a supply route.
Six months earlier, the chief political turning point of the war had been the Emancipation Proclamation. In spite of its imperfections, this made official what had to this point only been an implicit subtext (though the root cause) of the war: the abolition of slavery. It made recognition of the Confederacy by Britain and France highly unlikely, if not impossible. The oligarchies of both those countries had up to then been pro-Confederate, but even they could not oppose Lincoln's government now that it was explicitly anti-slavery. And the Proclamation made possible the recruitment of African Americans to serve in the Union Army.
An additional turning point I would mention is one not often recognized. In June, 1864, after the huge losses he had taken at the Wilderness, Spotsylvania, and Cold Harbor, Grant still managed to slip his army across the James River, which led to the essential entrapment of Lee's forces. Lee himself recognized that from this point on, the war would devolve into a siege and that there was little if any hope for his victory. Given Sherman's taking of Atlanta just over two months later, Sherdian's destruction of the food supplies in the Shenandoah Valley, and then Lincoln's re-election in November, the Confederacy was doomed.