Looking up your online financial info is not good enough. You need to download all statements, check images, year-end statements, etc. to your computer so you can view them offline anytime. That's the only way you can keep all the info since the beginning of time. That's why these websites let you download these things. Utility bills, phone bills, internet bills, everything. Some of these websites give you as little as 3 months' time to download documents before they are gone from the websites.
EDIT:
Emails need to be saved offline as well. Hillary Clinton may have given saving emails a bad name, but it is actually a good thing to do. Email services like Gmail have a cap amount of storage, beyond which you have to start deleting emails. The only way to save every email is to store them offline using a separate email program on your computer, such as Thunderbird or Windows Live Mail. It's a bit tricky technically to save them offline, however.
EDIT #2:
After you saved all these important documents to your computer, it still isn't enough. You need to back them up somewhere else lest disasters, floods, thefts, or hardware failure occur to your computer. Your backup should be put somewhere that is preferably not your home, such as the Internet, the cloud. There are many cloud storage service, such as those by Microsoft, Google, etc., that let you store gigabytes for free, or terabytes for a fee. And you need to do these backups regularly, of course.
