I'm not sure if Google would even want to support the DropBox model, which makes desktops play nice with the cloud, whereas Google would rather have the desktop die. EDIT: Looks like Google does allow 3rd party apps to implement desktop sync though.
Scenario1: Dropbox will have no other choice but switch their client to support google's API and, consequently, lower the price. They will gain a new load of customers and do fine.
Scenario2: google acquires dropbox. See scenario 1
Scenario3: google releases their own sync client/dropbox clone. Dropbox dies. Google wins doing evil (is competition evil?)
Scenario4: Google does like Pontius Pilate: releases API and let the market decide. Dropbox still likely to win.
Did I miss anything? It seems to me Dropbox has 1/4 chance of getting screwed, 3/4 of win.
2: I think the likelihood of this is low, unless Google does it to kill off dropbox.
3: I personally would probably use both, but for different reason, google's sync so I can remotely manage documents I want to use in google's apps, and dropbox for a quick and dumb file syncing for other stuff. I can see the competitiveness still working out here.
4: I agree, I'm a huge fan of dropbox, see #3 above.