South Carolina was the first state to leave the Union. It did so on December 20, 1860 with the unanimous vote of 169-0.

Mississippi 1-9-1861

Flordia 1-10-1861

Alabama 1-11-1861

Georgia 1-19-1861

Louisana 1-26-1861 (interesting note just three days later Kansas was admitted into the Union 1-29-1861)

Texas 2-1-1861

Tennessee 2-10-1861 (after first voting it down on 2-9-1861)

After the election of Abraham Lincoln in November of 1860, a number of states voted to leave the Union.  Many of them did this in early 1861.

South Carolina

Mississippi

Florida

Alabama

Georgia

Louisiana

All of these states left the Union in January of 1861.

Texas left the Union in early February of that year.  Missouri voted not to secede from the United States.  These are all the states that voted to secede from the Union before April 12, 1861.

The next state to secede was Virginia, on April 17, 1861.  The rest of the states seceded in May and June.