There are a number of companies that allow you to store files online for free ("file hosting services") for personal use, public sharing, or a combination of the two. These are sometime ad-supported and sometimes supported by a premium tier. Or else the company is just offering the service for good will and to build their brand.
Some that I've used and liked are:
Box.net - 1 GB, ad-supported, many features
SkyDrive - 5 GB, pretty easy to use, by Microsoft
DropBox - easiest to use once set up, automatic syncronization
YouSendIt - mostly for emailing large files (upload the file then email a link to the recipient)
Mozy - 2 GB, designed for data backup
There are, of course, others available.
I should also point out that your data are not necessarily secure as soon as you upload it somewhere else, such as to one of these sites. As well, there may not be any guarantees of availablility of your files, particularly with free services. That being said, I find these very useful.
Edit: SmashingDownloads has a more comprehensive list of free online storage options.