GDC Vault
Game Developers Conference records, must see for any game designer. Big part of the content is paid, though. But even in the free part, you will find a lot of useful knowledge.
Gamasutra
The biggest game industry online professional community. News, articles, blogs, forums, jobs, and many more.
Game Designers Vault
Great place for game design beginners, with a lot of useful links and tutorials.
Academia
If you’re looking for some academic knowledge about game design, this is the place. Just search “Game Design”.
DiGRA
Digital Games Research Association – another good source of the academic knowledge about games and game design.
GamesIndustry.biz
One of the best sources of information about the business side of the game industry.
Newzoo
One of the best sources of information about game market trends and research data. Detailed reports are paid.
Flurry Blog
Great source of the mobile game market research and data.
Coursera
Free courses from the world’s top universities (game design courses included). If you’re looking for the source of fundamental knowledge in different areas, this is the place.
TED
The best-known place, if you’re looking for new ideas, knowledge or just want some inspiration.