The first computer bug was actually a moth trapped in the contacts of a relay in the Mark II Aiken Relay Calculator. The moth is still taped in the log at the Naval Surface Warfare Center Computer Museum at Dahlgren, Virginia. After the moth was found, the word went out that they had "debugged" the machine. The bug was reportedly first identified and named by Lieutenant Grace Murray Hopper while she was on Navy active duty in 1945.

Courtesy U.S. Naval Historical Center:

Original Image
www.history.navy.mil/photos/images/h96000/h96566k.jpg

Grace Murray Hopper Information Page
www.history.navy.mil/photos/pers-us/uspers-h/g-hoppr.htm