* If you use Gmail, you could create a Gmail account whose only purpose is to fetch messages from your main account. Set up mail fetcher in the backup account and add the main account as a custom From address. This way, you'll be able to read all the messages from your account and even send mail.
* Add the backup account as a Google Talk friend from Gmail Chat or from other Google Talk interface. As a side effect, you'll have access to your shared items from Google Reader.
* For Blogger, add the backup account in the blog authors section: Settings > Permissions > Add authors. The account should have admin privileges so that you can create, edit and delete posts.
* In Google Analytics, go to Access Manager and add the account as an admin. You'll have access to all reports and profiles in the backup account.
* Google Calendar lets you share the main calendar with other people and even give them the right to edit events. Click on "Manage calendars" at the bottom of the window, share the main calendar and add the backup account. You should select "make changes and manage sharing" from the drop-down.
* If you're the owner of a group in Google Groups, go to the member invitation section, select "Add members directly" and add the backup account. Then change the membership type of the new account to "owner". It's also a good idea to select "no email" in the subscription type.
* Add the backup account as a collaborator for some of the most important Google documents and notebooks.
* Other Google services only allow you to export your data: Google Reader (Settings > Import/Export), iGoogle (share each tab with the backup account), Gmail contacts, Google News personalization (scroll to the bottom of the homepage and click on "Share your personalized news with a friend").
The backup account will not have all the data from your main account, but you'll still be able to read your email, send messages, publish blog posts, check your calendar, add new events, access important documents etc.