Classic Programming Examples

As I was coding Conway's Life onto my recently bought TI-89, as a follow-up to doing a prime numbers program (shown as an Ulam's Spiral), I had the thought that "Life" must be the "Chopsticks" or "Fur Elise" of Real Computer Programmers-- /anyone/ can do a "Hello World", but only those people who're committed programers ever know about (and implement) examples of Conway's Life on a system they're learning about.

What other programs can people suggest would fit in that category? (I haven't know many others who do my personal Sieve of Erastothenes 'hello world'..) A Mandelbrot calculator is probably another example...

>>3
But almost every first-year-dropout Arts student has heard of Raytracing, and I once did a 2nd-year Maths Geometry subject that covered all the basic theory (sans surface properties & etc., but enough). "Conway's Game of Life" and "Towers of Hanoi" are examples that're practically only known to Programmers..