1861
Skirmish at Farmington, a few miles south of St Louis, Missouri.

Six blockade runners were captured off Galveston, Texas.

Skirmish in the vicinity of Harper’s Ferry, West Virginia.

U.S. President Lincoln, in a speech to Congress, stated the war is..."a People's contest... a struggle for maintaining in the world, that form, and substance of government, whose leading object is, to elevate the condition of men..."   He subsequently issued a call for an additional 400,000 troops.

1862

The following are appointed Federal Major Generals:  Darius Nash Couch, Philip Kearney, Alexander Mc Dowell McCook, George Webb Morrell, John James Peck, Fitz John Porter, Israel Bush Richardson, John Sedgwick, Henry Warner Slocum, and William Farrar Smith.

Day one of Colonel John Hunt Morgan’s (CSA) first raid into Kentucky.

Federal bombardment of Vicksburg, Mississippi, continues as Federal authorities puzzle over how to reduce the fortress on the Mississippi River bluffs.

Skirmish at Port Royal, South Carolina.

Confederate attack on Federal vessels near Velasco, Texas.

Federals capture the Confederate gunboat, CSS Teaser, on the James River in Virginia as it attempted to launch an observation balloon made of old silk frocks.

Skirmishes at Harrison Landing and at Westover, Virginia.

1863

Battle at Helena, Arkansas, that included the US ironclad, Tyler, as Federal forces repel a Confederate attack.

Skirmish at Green River Bridge, some times called Tebb’s Bend, Kentucky.

Skirmish at Emmitsburg, Maryland

Skirmish at Messginger’s Ferry, on the Big Black River, in Mississippi.

Skirmishes  at Cassville and Black Fork Hills, Missouri

Skirmish with Indian near Fort Craig, the New Mexico Territory.

Skirmishes at Fairfield Gap and Monterey Gap, Pennsylvania.  General Lee began to withdraw his forces away from the Gettysburg area of Pennsylvania making his way toward Virginia

Skirmish at University Depot, Tennessee

Skirmish at the South Anna Bridge, on the Richmond and Fredericksburg Railroad, north of Richmond, Virginia.

Skirmishes at Fayettesville and Huttonville, West Virginia.

Surrender of Vicksburg. Mississippi.  The Confederacy suffers its second major defeat in as many days when General John C. Pemberton (CSA) surrenders to Union General Ulysses S. Grant at Vicksburg.

The Vicksburg campaign was one of the most successful campaigns of the war. Although Grant's first attempt to take the city failed in the winter of 1862-63, he renewed his efforts in the spring. Admiral David Porter had run his flotilla past the Vicksburg defenses in early May as Grant marched his army down the west bank of the river opposite Vicksburg, crossed back to Mississippi, and drove toward Jackson. After defeating a Confederate force near Jackson, Grant turned back to Vicksburg. On May 16, he defeated a force under John C. Pemberton at Champion Hill. Pemberton retreated back to Vicksburg, and Grant sealed the city by the end of May. In three weeks, Grant's men marched 180 miles, won five battles, and took 6,000 prisoners.

Grant made some attacks after bottling Vicksburg, but found the Confederates well entrenched. Preparing for a long siege, his army constructed 15 miles of trenches and enclosed Pemberton's force of 29,000 men inside the perimeter. It was only a matter of time before Grant, with 70,000 troops, captured Vicksburg.
Attempts to rescue Pemberton and his force failed from both the east and west, and conditions for both military personnel and civilians deteriorated rapidly. Many residents moved to tunnels dug from the hillsides to escape the constant bombardments. Pemberton surrendered on July 4, and President Lincoln wrote that the Mississippi River "again goes unvexed to the sea."

You might find it interesting that the citizen of Vicksburg, MS,  would not celebrate the Fourth of July for the next 81 years. It was not until the end of World War II that the 4th of July would be recognized as a legal holiday by the citizen of that city.

1864

Skirmish in Searcy County, Arkansas.

Multiple skirmishes at Ruff’s Mill, Neal Dow Station, Campbellton, Mitchell’s Crossroads, Burnt Hickory, Vining Station, and Rottenwood Creek, Georgia.  Once again Confederate forces withdrew to newly prepared positions.  This time they were on the Chattahoochee River.  At one point, Federal forces were closer to Atlanta than Confederate.

Skirmish at Cross Bayou, Louisiana.

Skirmish in Clay County, Missouri.

Fight at Battery Pringle, located on James Island, South Carolina.

Beginning of a Federal expedition down the Mississippi River from Memphis, Tennessee, to Grand Gulf, Mississippi.  Transportation provided by the steamers, Rose Hamilton, Madison, J.D. Perry, JC Snow, Silver Wave, Sunny South, Tycoon, and the Shenandoah.  Skirmishes occurred at Bolivar, Utica, Port Gibson and Grand Gulf, Mississippi.

Skirmishes at Frankford, Patterson’s Creek Bridge, and South Branch Bridge, West Virginia.

References:

The Civil War Day by Day, Philip Katcher.
The Civil War Day By Day: An Almanac 1861-1865, by E. B. Long with Barbara Long.
The Chronological Tracking of the American Civil War Per the Official Records of the War of Rebellion, by Ronald A Mosocco.
http://www.history.com/this-day-in-history.do
http://www.on-this-day.com/cgi-bin/otd/uscivilwarotd/uscivilwarotd.pl