EDSAC (Electronic Delay Storage Automatic Calculator) was one of the very first computers ever created. It ran its first programs on May 6, 1949 calculating table of squares and a list of prime numbers.
Martin Campbell-Kelly of the University of Warwick, England, created a neat software to simulate the EDSAC computer you can download and play with:
The Edsac simulator is a faithful software evocation of the EDSAC computer as it existed in 1949-51. The user interface has all the controls and displays of the original machine, and the system includes a library of original programs, subroutines, and debugging software. The simulator is intended for use in teaching the history of computing; as a tutorial introduction to the classic "von Neumann" computer; or as an historical experience for current computer practitioners.
Link (Thanks Cary Groneveldt!)