This isn't the first time the topic has come up, which makes sense, given how long we've been in beta. In November 2010, we talked a little bit about how to get our numbers up. One of the 15 "Top 7" questions is about how to promote the site.
And it's a problem that all beta sites deal with. Some just deal with it better ... and some have an easier time of it because of their audience. (Arqade, for example.) Either way, our goal has to be reaching a sustainable volume of good questions that can get us out of beta: if we seed questions, at some point we'll run out. If we lower the quality threshold, then even if we do get out of beta, we become just another site, with the added bonus of having to explain why these old questions were all closed while these new questions are allowed.
I think Alex has the right idea - more people asking more questions about more games. goldPseudo touches on some of the problem, that there are a lot of games that are designed not to bring up questions. (Chutes and Ladders, right?) But there are plenty of games that do bring up questions, as we've seen with MTG. We just need to tap those audiences (uh, not in a MTG sense), and that means pretty much the same thing it does for everyone else.
Individually, we can promote the site through social media, especially by posting questions that need answers. We probably all are connected to people who play games but aren't here yet, and maybe seeing a question they can answer will draw them here. We can remember to ask questions here when they come up while we're playing games ... but again, these should be good questions, not questions-for-the-sake-of-asking.
I also like Pat's suggestion from the Top-7 question: work with cons when we can. Drawing questions from attendees themselves is a great idea, although we would have to emphasize that they won't necessarily get an immediate answer (i.e. we're not a replacement for GMs) even if we make more of an effort to watch for questions during cons.
If there is a smaller con in your area, you might be able to work with the mods and SE so that BCG can be represented there. (Larger cons probably require more advance planning and more work. I've been looking for an excuse to go to Gen Con, which is local to me, but as Pat points out, the ROI for us may not be worth it.) In a sense, game nights at home are baby cons: we can use those as an excuse to post questions here when they come up (again, real, high-quality questions, not things like "Can I move forward with a 4 in Sorry?"), and maybe get one or two new people to check out the site as well.
All that is really about time and effort. Anything else is just fool's gold: there is no point in getting out of beta if we do it as Yahoo Answers 2.