I'd like to see the SL client itself become more like the decks in Snow Crash, where you have local storage (limited to stuff you have _full_ rights over (all the way down to the turtle)) and the ability to run far more powerful local applications. It would actually be fairly easy to map arbitrary applications to a special local texture (like the media texture) in Mac OS X or Linux, and probably not that hard to do it in Windows, though interaction with them would probably require an explicit focus and switching to a "work mode" where the application is more like a HUD object than an in-world one.
That would still be tremendously useful, though, particularly for objects you just want status from, even without the "work mode". Of course other people wouldn't see these apps, or would see their own apps on the "application textures" if you picked a common one, but of course that's got advantages as well as disadvantages.