With the release of Office 2013 and it's emphasis on SkyDrive storage, I've had several people ask about moving their pst file to SkyDrive, DropBox and similar services.
The answer: It won't work. Outlook puts a lock on the pst file when the pst file is open. SkyDrive (and other cloud solutions) continually syncs the local folder. It won't be able to sync the pst because Outlook has a lock on it and as a result, the pst file could become corrupted and data loss occur.
While you could use SkyDrive or another cloud service to store backup copies of your data files, its not recommended due to the large size of many pst files: uploading a large data file can take "forever".
There are online backup services that can backup pst files when Outlook is open and incrementally backup the pst, so only changes are saved. These are safe to use because they are designed to work with Outlook data files. However, unlike backing up a file to SkyDrive or DropBox, you can't download the pst file to another computer or when needed. You need to restore it using the backup application.