Who were the generals of the North and South during the American Civil War?
Perhaps a more appropriate answer would be the Commanders in Chief of the North and South, other than the President himself. There were, of course, many subordinate generals who were also important, but whose place in history is more trivia than consequence. The South had only one commander in chief; Robert E. Lee. Lee had previously been offered command of Union forces by General Winfield Scott, but had turned down the offer as he could not bring himself to fight against his native Virginia. He later resigned his commission in the U.S. Army and joined the Confederate cause.
Lee managed to defeat most of the Union commanders in chief who were routinely removed from command after their defeat; this in accordance with standard army policy. The first commander was General George McClellan who was fired after Bull Run. Later, General U.S. Grant was defeated at Shiloh by Gen. Albert Sidney Johnson on the Confederate side. Grant was removed and replaced by Henry "Old Brains" Halleck. Halleck was defeated by Lee and replaced with McClellan once again. McClellan was too timid to attack Confederate forces following a Union victory at Antietam, and was fired a second time, this time permanently, and replaced by Gen. Ambrose G. Burnside. Burnside wore his whiskers far down his cheeks; thus the term "sideburns." Burnside was defeated by Lee at Fredericksburg and ultimately replaced with "Fighting Joe Hooker." Hooker was defeated by Lee at the Battle of Chancellorsville, and replaced with U.S. Grant once again following Grant's victory at Vicksburg and who prosecuted the war to its conclusion.
Of course, there were large numbers of generals on both sides in this war. For the purposes of this question, we will look at a few of the most famous ones.
The generals who were (by the end of the war) the most important on each side were Robert E. Lee for the South and Ulysses S. Grant for the North. Grant, however, was not the first of the chief generals for the Union. His most famous predecessor was George McClellan, who was eventually fired by Lincoln for not being aggressive enough.
Some other important Northern generals were William T. Sherman, George Meade and Philip Sheridan. Some other important Southern generals were Nathan Bedford Forrest, Thomas "Stonewall" Jackson, and Pierre Beauregard.
There were so many other generals who were important at various times and places, but this is a short list of some of the more famous Civil War generals.