This is by no means a complete or authoritative listing. These are just a few sites I've found useful over the years (years? yikes!) I've been playing the game. When I first started, I had no idea there were resources outside the official WoW webpage. While there was a lot of helpful information there, I floundered around for quite a while, till I found the first site that provided me with some tips and guidance, with walkthroughs for many quests, and tips from users who'd been there before. That first site was Thottbot, a fairly rudimentary website with some useful details about items and NPCs. More useful than Thottbot, at least when I first found it, was Allakhazam, a site that offers guides, tips, and item info for several MMOs aside from WoW. Allakhazam was my go-to site for almost a year, until Wowhead came along. Wowhead, like Thotbot, had a clean, simple, search-based interface, but its user-generated tips and walkthroughs were much more detailed, on a par with. and usually surpassing, those on Allakhazam. But even Wowhead had its limitations, so when I wanted more information, or deeper insight into the background and lore of the game, or fuller walkthroughs, including strategies for quest chains, I turned to Wowwiki. Like Wikipedia, it's a user-generated website, with articles written and edited by the users. A great site for general information, though, like any wiki, it has its odd blind spots.
Allakhazam, Wowhead, and Wowwiki: Those are the three main sites I use, but there are others that I've found helpful, and here's a quick list:
Curse Gaming, for mostly-up-to-date WoW add-ons.
MapWoW, for lovely maps of Kalimdor, the Eastern Kingdoms, and Outland, based on the terrain-relief maps found in the onscreen mini-map.
WoW Insider, a blog-type site for news, commentary, community, and extensive guides to classes and professions. (A must read if you're struggling to understand how to play your class, whether it be a mage, a hunter, a warrior, etc.)
Ten Ton Hammer, another general-purpose MMO site, with an excellent WoW sub-site.
And finally, Warcraftmovies, a great site for fan-built machinima -- short movies using WoW in-game animation. Lots of fun, though leaning heavily toward in-joke humor.
That's it. By no means a complete, or even extensive, list. Consider it something to get you started.