Interesting Exercises?

There have been some programming exercises I have done which I've found really interesting, and was hoping for some suggestions on some more exercises I could try out.

The ones which I have completed so far are:
Sudoku Solver
Sieve of Eratosthenes
Lucas-Lehmer primality test for mersenne primes
Recreate the scene from 'Sneakers' where they decrypt the federal reserve transfer node
Output pi to n decimal places
Output the Fibonacci sequence
Calculate the Julian Day Number
Simulate the enigma machine, using the exact same wiring as they did in WWII
Texas holdem pot odds calculator (might be illegal)
Create a dope-wars style game

Some ideas I've had but can't think of how to implement them:
Sort 1 million 32 bit integers using quick sort or merge sort (I understand the algorithms, but can't think of a way to implement them)
Something involving neural networks
Simulating genetics/natural selection
Simulate the weather (in a very simplistic way, I'm not going to write the next GFS or NAM)
Simulate the stock market

Does anyone else have any interesting ideas, or ideas on how to implements those ideas above?

Thank You :)
-Sam

Do you know Project Euler or UVa Online Judge (just google for them)?
They have tons of interesting and challenging exercises! Project Euler is very math-intense, depends on you if that's good or bad :)

I was trying to get onto project euler the other night but there was an error on the website, I will check them out, thank you :)