My big catch phrase about mobile computing is "offline anywhere". The mobile network, so far, is too slow, unreliable and limited for a lot of common tasks, so the way I want to go is to take those tasks and make them available offline, using bandwidth when they can (preferably WiFi to save on extortionist 3G data costs) but working without any network connection at all most of the time. For a lot of web services, it simply isn't necessary to have a constant network connection. An action list, for example, can live on your phone, but as long as it keeps in sync when a WiFi network is available, you don't need the website itself most of the time. Any commands you issue will simply take effect on the server's database the next time the app connects, and that's fine.
When you're dealing with a small amount of data that doesn't have to be 100% up to date right now, if you're not using a small offline database with occasional sync, you're doing it wrong.
Mokalus of Borg
PS - I don't expect this to be the case forever. We're always building better networks.
PPS - It's just that the mobile data network has the most room to grow.