I honestly believe that with maybe the exception of OSs and browsers, everything will be a web app within the next 10 years. Having said that, let me clarify that by everything I mean everything that a) involves a UI of some kind and b) can be guaranteed secure.
User-interfaced apps will always at some point need a backend, which will at some level require code that is not being interfaced by humans and not being executed via HTTP. I am always reminding myself that things like 'cat' in Unix are actually programs that the OS is calling, not just a function built into the OS. MySQL won't be a web app (as far as I know), but app that powers web apps. We may get to a point where these apps are fully developed via a web interface, written, audited, uploaded and called all via a browser, but at some level its still running behind the scenes.
On that second point, about guaranteed security, I can very easily imagine a large corporation or government office running 95 percent of their daily routines via web apps, but mandating that certain high-security operations be done on a machine directly interfaced with some sort of mainframe, after passing through the cool doors with the retinal scans and what not. Or simply because they can't risk moving certain mission-critical apps over to the web, from fear of it breaking our losing data in the process.
But with those two things aside, I honestly believe everything will be web-based. With the advancement of Web Services and XML in general, it will be possible to not only access and interact with our data, but to plug our custom apps into another app and extend that interaction further and in any environment we want.
It's like that Apple ad "There's an app for that." Except once people get the real picture, it won't be an app written for your iPhone, but a URL. "There's a site for that."