Its very important. With all these web 2.0 online apps coming out (Gmail, Google Reader, Remember the Milk) it is important to be able to access their functions while you are offline. Google Reader offline mode is great because you shouldn't need to be connected to the internet to view mostly text, so offline mode makes sense for that. Instead of a while desktop application, you just enable offline access, which you can make changes in the app and sync it right back to the online app. This is beneficial because it still means users are inside the online app which they can access from any computer, not just the one that the app is installed on.

The same thing goes for Google Calendar, and Gmail. Wouldn't it be great to be able to add things to Gcal and read/write in Gmail without being connected (these don't actually have GG functionality yet *tear*)? How about Google Docs, which has GG functions in the testing phase. The ability to access your documents not only from any computer, but offline as well when you need them, then have it all synced up quickly has a very strong appeal. GG and offline access pertains to me and others in many ways, but I could see it seeming like not a big deal if you don't have many things that require that offline access. For some of us though it couldn't be more useful : )