You probably know about the support forum at wordpress.org. It’s the first place to go when you need to find an answer to a question or to see if other people are experiencing the same weird problem you’ve encountered. Of course, there’s also the Codex, and, as of 3.0, the Help tabs at the top of each screen are now filled with useful, contextual information.
Where else can you go?
IRC. There are channels for WordPress, BBPress, and BuddyPress on Freenode. Just keep in mind that the -dev channels (like #wordpress-dev) are for discussion about changes to the core, not for general questions. (Also, there’s a scheduled developer meeting once a week. Don’t interrupt it with a question that’s not on the agenda; you’ll get a brusque request to leave.) The WordPress channels are like anywhere else on IRC, which is to say that some days, there are lots of helpful people hanging out, and other days it’s a wasteland. Be patient.
Trac. This is the ticket system for the WordPress project. It contains bug reports (and often solutions or workarounds) as well as ideas for new features. If you really think you’ve encountered a new bug, write it up here! (See Reporting Bugs on the Codex for instructions on using Trac and tips on writing good tickets.)
The source code: Xref. The WordPress source code is, for the most part, pretty well documented — especially the newer functions. For example, here’s the internal documentation for the register_post_type() function currently in trunk. If you know enough PHP to follow along, reading the source is the best way to really understand how core functions work.
Google. OK, this one’s obvious, but you’d be amazed at how often people overlook it. If you’re getting an error message, copy it into the search box surrounded by quotes (so Google looks for that exact phrase). If someone’s solved that problem before, chances are they blogged about it or posted something about it in a forum.
The Tavern. Jeff Chandler has built a forum to go with his weekly podcast, and it’s a great resource. It gets less traffic than the official forum, of course, but there’s also less noise. It’s also a fun place to kick back for a few minutes — check out the alphabet game, among other things.
The WP-hackers mailing list. Many of us have a love/hate relationship with WP-hackers. Some weeks, it’s full of great discussions, and some weeks it gets bogged down in silly personal disputes. In other words, it’s just like any other high-traffic mailing list. The hackers list is intended for developers working on plugins, themes, or the WordPress core code, so it’s not a good place to ask a beginner question, but if you’re working on something more advanced, feel free to join. You should search the archives to see if your question has come up before (and to get a general idea of what’s discussed on this list).
Ask Mark Jaquith. Mark is a core developer, and will round up questions to answer in his blog. Here’s the latest batch, for example.
WP Questions. This is a relatively new resource, but there are some great answers in the archives already. Note that this site works on a bounty system, so if you’re asking a question, you’ll be expected to pay the person who comes up with the best answer. Personally, I’d save this as a last resort, since there’s so much free help available elsewhere, but this seems to be a good place for answers to really tricky questions.
Those are just the resources I use. I know there are lots more! Feel free to suggest your favorites in the comments.
Don’t forget wordpress.stackexchange.com. While this site is still in its beta phase, there are some really good answers already.
Our little-known support forum for heavier multisite related questions is at http://musupport.net. it’s paid tho.
Great suggestions. Thanks!