For example we just launched Prime, an iPhone app that allows you to download your medical record from any doctor and share health activity with friends and family. http://stayinyourprime.com. We're not the only ones in healthcare. There's also Practice Fusion, drchrono, DoctorBase, and countless others.
And on the education side there's Inkling, for example. And on the banking side there's Simple (though they're actually based in Portland). And of course YC famously backed Watsi. Maybe you have different examples in mind of what big problems are but it does seem to me that as we are seeing more startups overall that means we're seeing more startups addressing bigger/more meaningful problems.