The first idea that comes to mind for me is this:
I'm a programmer, unfortunately. I discovered Stack Exchange through Stack Overflow. But I knew about Stack Overflow for almost a year before I realized it was part of a network of other sites, and actually made an account.
I had come across SO by google searching the programming problem I was having, finding a previously asked question, and reading the answer. Given the frequency with which I google programming-related bugs, problems, dilemmas, and so on, I barely pay attention to the context of the answer. At first it was just another google result. After a few times, I did of course realize that SO was repeatedly the source of my solutions, and I paid more attention to it.
That was the day I noticed the "Ask a Question!" button.
And that was the day I discovered the rest of Stack Exchange.
So here's my idea, and I'd love to hear others: Visitors come across our sites in google results, but, being unfamiliar with SE's methodology and rich resources, they peruse that one result and then leave.
They fail to grasp that if the page they found didn't answer their question, they can just ask a more specific question and get a great answer, or search for similar questions. They leave, and maybe a lot of them don't end up coming back, because in many fields and subjects our sites don't come up as frequently in google results as SO does for programming problems.
I think we need to figure out a way to make people realize what they've stumbled upon. Maybe even as simple as making the "Ask a Question!" button bigger. Until I really started paying attention that one day, I never even noticed it. It was just part of the nonsense surrounding the little rectangle of content I needed. When I'm searching for programming answers, I'm in the habit of going fast and ignoring the perimeter of the central content, which is very rarely pertinent. I think this may apply to many people, especially those who are less internet-savvy.
Because, simple example, Spanish.SE is getting 1.8 questions a day, and I know an awful lot of U.S. high school students who just cannot grasp the Spanish they are being made to learn, and would die to find this site.
(But then again, Spanish also has low traffic. Perhaps if established users made a point to modify question titles into clearer forms that might be more likely to come up in Google results? Attract more people, then make them remember the site's name and feel that there's reason to come back.)
Remember, before there was Stack Exchange, there was Yahoo Answers, and its horrifically inconsistent quality left an awful lot of people jaded towards Q&A sites. We have to counter the possible presence of that attitude in newcomers.