When I have a problem running the bitcoin client, where can I go to get help? Let's assume that either a bug report exists already, or the problem is unlikely to be caused by a bug.

What I know so far is:


This site will be appropriate for some support questions, and the mechanism for the site encourages peer review of each answer. Here's an example of a support question.
The bitcointalk forums have a technical support category that is likely to give a good response as there are lots of active users.


Where else might I get timely support? (paid or unpaid)
I think you have mentioned them all:

bitcointalk, 

bitcoin.stackexchange, 

github issues page, 

bitcoin-dev.

For commercial companies offering bitcoin client support see Stephen Gornick's answer.