Here is a Mathematica file that implements the Doomsday Rule as well as Conway's rules for computing Easter and Rosh Hashana.
One advantage of being proficient with the Doomsday Rule is that you can spot calendrical mistakes in books and movies. Here is a short collection of day-of-the-week bloopers that I have noticed.
For another account of the Doomsday Rule, see Rudy Limeback's site.
Conway once told me that he developed the Doomsday Rule when Martin Gardner showed him Lewis Carroll's perpetual calendar algorithm and challenged him to come up with something simpler.
For an extensive discussion of calendar computations, see Claus Tøndering's Calendar FAQ.