This is a partial list which grows from time to time.
Names in blue link to biographical sketches.

The list is complete for Company H and for field and staff officers. A number of names remain to be discovered, verified, and added to this list (as of June 2009). The list is nearly complete however for Franklin, and nearing completion for Chickamauga. It is ordered by time period/battle and then by company; thus it begins to give a picture of which companies were in trouble where. It's no secret that the regiment was most tangled in enemy lines at Chickamauga on the second day and Franklin in the first hour—and in both cases due to generals' decisions that reflected a failure to grasp and handle battlefield situations. There are related narrative pages on this site:
A Persimmon Tree: The 51st in Confederate Prisons
Theo Eads: One of Last to Leave Andersonville
Lyman Needham: Letters from Danville Prison
Martin Riley's Account of Captivity in Confederate Prisons

Sources:

Compiled Service Records, National Archives and Records Administration, Washington, D.C.

J. N. Reece, ed., Report of the Adjutant General of the State of Illinois, Reports for the Years 1861-66, revised, 8 volumes, Springfield: Phillips Bros., 1900-02, Vol. I, pp. 189-202.

*Note: Elon Clark was not always followed and overtaken by good luck—or maybe he was. He was wounded slightly at Stones River. A few weeks later, while on picket, he shot one of his fingers off. At Chickamauga, he was wounded along with many of his Company K comrades on the 19th and taken prisoner on the 20th (though he does not appear on the casualty list at all). He was imprisoned in Richmond at the end of September, but he was soon admitted to the prison hospital (for causes not specified). He was not transferred on to Danville, Virginia in December as were most of the Chickamauga prisoners of the Fifty-First. On March 28, 1864 he was paroled at City Point, Virginia and sent to parole camp at Benton Barracks, Missouri. He was soon exchanged and returned to the regiment in time to be captured in Georgia at the Battle of Peach Tree Creek on July 20, 1864. He was sent to Andersonville. Andersonville records show that he died there on September 4, 1864 and was buried in Grave No. 7760. His military service records show both that he died and was buried at Andersonville, but they also indicate that he survived and was discharged in February, 1865. There is a pension file which clears up the matter and shows that he lived until May 24, 1880 and then died in Iowa.

**The "N. E. Ferry" was a parole point on the Black River, just outside Wilmington, North Carolina, in Berite County. It was most often the point of parole for Federal army men who had been imprisoned at Salisbury, North Carolina or Florence, South Carolina toward the end of the war.

***Captured while traveling from Nashville convalescent camp to home in Illinois.