How do I store all my documents online?

I believe Google Docs is relevant to your needs. It doesn’t function simply through “saving stuff in folders on [your] computer,” but if you use their browser-based office suite (instead of MS Office), that is quite possible.

There is an add-on for Firefox that allows you to save files on gmail, up to your limit for free, and you can always buy extra space. Other on-line servers generally charge a fee.

Dropbox is what you want.

I use Mozy to back-up my computer. For five bucks per month it backs up your entire computer. It just works in the background and you don’t really notice it doing it. It is a cheap way to know that everything is safe.

There is Dropbox too. It works like a folder on your computer and you just drag stuff over to it. And you can make folders public. There is a free account for 2GB. And 50GB is ten per month.

with johnpowell on Dropbox we use it at our offices unlimited sync with multiple machines and all platforms free account gives good storage and most importantly the sync is on the fly immediate!

I use Dropbox myself, but I thought the OP asked for something that was free.

Another vote for dropbox and Google Docs. Google Docs maybe what you looking fro as opposed to dropbox which requires installation.