I use online banking (though I go to the physical bank for check + cash deposits and seldom use credit cards). However, the bank only has access to info on my account with them, not all accounts I have.
And yes, I think that users of mint.com are f**kin’ idiots. I do my taxes using desktop tax software, not by uploading personal info to some website.
Office is an example of an application where you have choice. But many other apps don’t give you that choice, or are murky about where data are stored.
And with some mobile devices (iPad), it’s hard to transfer data from certain apps on them unless you’re doing so via the cloud. Harder than it needs to be, IMHO.