Below are links to resources for the major disciplines in game development. Each one provides a unique community, resource, or tutorials to help you get started in game development.
Programmers - Great communities and resources for coders:
http://www.gamedev.net/ - Good community for coders.
http://create.msdn.com/en-US/ - Great resource for developing games and apps
https://www.dreamspark.com/ - A solid resource for students. Lots of free software here.http://altdevblogaday.com/
Thanks to Kristopher Velez for more programming resources.
Artists - 3D to Concept:
http://www.cgsociety.org/ - Great for seeing how professionals from the movie and game industry make their art. Also a solid community.
http://www.game-artist.net/forums/ - An awesome community of developers and people who are learning how to be a 3d modeler. Great support.
http://forums.sijun.com/ - Wonderful community for 2D artists.
http://www.polycount.com/forum/ - This community has great challenges for 3d modelers. Want to push yourself? Then compete against professionals.
http://cg.tutsplus.com/ - Great website for learning how to model. Pick up some neat tricks here.
http://www.gametrailers.com/ - For the reviews. Why are the reviewers saying this?
http://penny-arcade.com/patv/show/extra-credits - Great website for designers
Business - This is something that designers and the other disciplines need to watch. More for designers as games are starting to incorporate money making strategies as part of the gameplay.
http://penny-arcade.com/patv/show/extra-credits - Great website business people. Need to know what is going on in the design community. They also talk about core issues that are happening in the industry.
http://www.industrygamers.com/ - This site provides a solid business look to the game industry. A must read.
http://venturebeat.com/ - This site provides a look into which companies are being funded, by who, and their impact. Great for the all around business, but also has a site designated to games, "Gamesbeat".