From PerlNet

This is a list of programs every programmer has written from scratch at one point. By "every" we don't mean everyone, just that it's a general trend for enthusiastic hackers to write one or more of these at a point:

1. Hello, world ;-)
2. An Interpreter for Scheme (a relatively minimalistic dialect of Lisp)
3. A templating system or HTML preprocessor
4. A database abstraction layer, or Object-Relational Mapper (ORM)
5. An IRC bot
6. An interpreter for his own language (possibly embedded in text)
7. An ad-hoc Content Management System (CMS).
8. A program to calculate the digits of Pi.
9. A prime numbers-related program (prime factoring, prime generation, etc.)
10. A "build system" (normally just a makefile generator).
11. A program to render the Mandelbrot set.
12. A simulator for Conway's Game-of-Life.
13. A Tower of Hanoi program (also in any programming languages he has learned).