According to these notes from Google’s Analyst Day Power Point presentation, GDrive is definitely on the horizon. This new service will let you store just about any file and access them from anywhere. Like other Google services (Video, Maps, etc.), GDrive will most likely have a basic (free) membership along with a variety of upgrade (paid) options.
“With infinite storage, we can house all user files, including: emails, web history, pictures, bookmarks, etc and make it accessible from anywhere (any device, any platform, etc). We already have efforts in this direction in terms of GDrive, GDS, Lighthouse, but all of them face bandwidth and storage constraints today.” excerpt from Analyst Day presentation notes.