This will make a great class action suit against Target. After all, when did you give them permission to start tracking your purchases when you use a credit card? We worry about online privacy at Google or other companies this is worse. It is not as if you are using one of those cards at the grocery store where you agree to allow them to track your buying habits.
I think a lot of people are already using Google Docs as the mythical "G Drive." I use it for that purpose and store all my photos, videos, docs, etc. up there. In fact, it will even stream your videos like youtube (I cannot speak to audio as I am not a big music person).
My complaint is not that is cannot store anything you want, but that it is not integrated with their own products. If I am storing something, like a photo, in Google Docs, I should be able to publish it to Picasa or Google+, or even attach it to an email (either from the email or through Google Docs). Same with video, except this time youtube instead of Picasa.
Instead, I have to download it first and then upload it to the appropriate app.
I don't use DropBox, but I have heard it is great. But, I do use a product: https://www.insynchq.com/ to back up and sync my Google Docs locally. I don't know if that is the same.