Game Programming Software
For anyone new to the idea of programming games, I highly recommend starting out with DarkBASIC Professional Free by The Game Creators. DarkBASIC is an easy-to-understand programming language and allows you to experiment with game programming first hand. You'll learn the basics and fundamentals of programming quickly with the help of the TGC Forums and with these excellent beginner's tutorials!
If you are already familiar with the fundamentals of programming and want to try your hand at a higher-level language, I recommend going with Microsoft Visual Studio C# and then downloading the XNA Game Studio package.
Artsy Software
3D Modeling/Animation: Blender.org has great software called "Blender". The newest version doesn't have DirectX support yet, but it will soon be implemented. Blender is a little complicated to learn, but it's free and will allow you to explore the 3D modeling/animation venue that's important for game creation.
Texture Making/Photo Editing: gimp.org GIMP (or "GNU Image Manipulation Program") is a fantastic free photo editing application with many professional features. This also enables you to make seamless textures rather easily, so I recommend it for both photo editing and texture creation.
