Everyone who's reading the Meta site has an interest in spreading the word about the site. That will increase the user base, give us better questions, and give us better answers. What kind of things should we, as interested users, do to let others know about the site? The "random googling" method is already going pretty well, but I suspect there's other things we can/should do. I'm also assuming we've already told our game developer friends about it. Or should we wait until the site is formally out of beta to do more full on evangelizing?
Social media outlets if you don't mind tweeting or updating your facebook status about the site if you think you have some followers/friends that would be interested in game development.
I put the word out on Slick2D's forums, which is a popular Java 2D gaming framework.
I think going to GameDev.net and Gamasutra too early will only exacerbate the relevancy/quality issues already present. I'd suggest actively targetting professional game developers somehow, perhaps by emails to tech leads, or similarly direct means. Might be worth talking to Develop, getting them to run an article in the magazine on it.
EDIT: On another note, I wanted to put up a post talking about the site on my company blog. It would be nice if there were a banner image I could use for the link - the nature of the HTML used on the page heading means I'm having trouble actually pulling the image off for use.
I think reaching out to the Indie communities that don't have a dedicated Q&A section would help drive people here. The initial endorsement from Jeff & Joel helped Stackoverflow (followed by the Google Endorsement for android) I am hoping that some of that magic can work here.
If you are active participants in any of the communities below (feel free to edit more in) then changing your signature or something to link to here would be of some help.
(Adding a new answer since the StackExchange guys are talking more about promotion of sites)
Personally I've always thought that face time with people is more effective an endorsement strategy than random internet stuff. And that's really what we should be thinking of it as, endorsing instead of advertising.
Most people who are active on this site should be a member of their local IGDA chapter. I'd recommend going to their meetings and talking about the site with the guys there. If there were fancy fliers or business cards that we could hand out, that would be even better. But it has to come from a "hey we're developers and use this site and think you guys might like it to" as opposed to coming from "outsiders".
I've tried telling people in the industry that I hang out with normally about the site, and gotten a few people interested in it and posting results. They've mostly been programmers, though.