Adobe Forums. A good community for answers to problems related to Premiere Pro, After Effects, Photoshop, and other Adobe products.
Audio Video101. A good dictionary and explanations.
Avid forums. This is an Avid-sponsored community that is always good for answers to bizarre questions.
DVinfo forums. This is my favorite AV forum site because it has forums on just about everything (hardware and software) and the professionalism, helpfulness, and friendliness of the community are all excellent.
Exposure. A WONDERFUL site specifically devoted to low-budget film and video production. It has some excellent tutorials and no-nonsense advice (e.g., see their primer on basic lighting technique).
Plug-in Manifesto. Their main job is to facilitate online video distribution, but they have great interactive production exercises and links to vendors, bulletin boards, etc.
Pro Tools LE forum. Like the Avid forum, this is a good place to find answers to obscure questions.
Toolfarm forums. A good place for help with Red Giant software (Magic Bullet, Instant HD); also has a good Adobe forum.
Videomaker Online. The official site for Computer Videomaker magazine. Limited, but with good articles in language that you don't have to have an engineering degree to understand.
B&H Photo/Video/Pro Audio. My standard source, with an excellent selection of used equipment.
Broadcast Supply Worldwide. BSW is a great vendor for audio gear.
Markertek. Sells the studio-oriented gear that B&H sometimes doesn't carry.
Photomart Cine-Video. Specializing in lighting and field production accessories.