Video game hacking is becoming an increasingly popular category for CTF competitions. Game hacking has been featured at CSAW, Nullcon, and even at DEFCON CTF. The following resources and tools are great for learning game hacking.
Cheat Engine Tutorials
While most tutorials included with free software is lacking, the tutorial included for Cheat Engine is actually really well done!
To start the tutorial, check out the section on Cheat Engine below! Start Cheat Engine, then click Help>Cheat Engine Tutorial.
Cheat Engine is a great, well rounded tool for hacking games. It includes a variety of features, including a memory scanner, debugger, disassembler, and more!