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...

>Towers of Hanoi is in a lot of video games too

Ah, you're right there.

>Have you ever actually programmed a raytracer though?

COMP380, Final Year Computer Graphics, 1992... Using Black & White XTerms to render internally 48-bit images was ;_;

A bogo-raytraced sphere (not actually photon-traced; just dot-products from the light) was one of the toy programs I wrote on the "Pascal" Unix machine for MATH1A/1989... which had _VT52_ (clone) terminals... I managed to get an animated "moon rise" happening within the 1,000,000 instructions limit.. Yes, in ASCII graphics.. :/