Google Gears is an interesting idea which is still in its infancy. I'm interested in the use of offline storage for web apps - you get the benefit of a regularly updated web application with locally stored data - which is interesting in terms of privacy. This could be more beneficial for application developers than for users, since it allows them to provide a central service but give their subscribers the option of keeping their data to themselves. For financial software, for example, this could be a boon.
Of course this does mean such applications lose a primary benefit of the web app - that of backup and the ability to roam. Keeping a user's data on their local machine means that they're responsible for their data integrity and for moving their data from machine to machine.
Most applications which use Google Gears won't come up against this problem, because they'll be syncing data back and forth between the local machine and the remote server (or will they?). But I think there's going to be a new breed of application which relies on the client a little bit more than we've been used to in the past.