Hmm for pictures I use SmugMug.com (Not Free) But fantastic for backing up those special moments.. Never had a problem with them for the past 2 years. I'm very skeptical about free online data storage websites.... The integrity and security is what keeps me from using them.. But if it's nothing important then I can see it as an option.
Dropbox is the bomb for online storage and backup. You get 2GB of space, but if you sign-up with a referral link you and your friend both get 250MB free. https://www.getdropbox.com/referrals/NTExNTI5Njk Shameless plug, but it's beneficial since we both get more space free without having to do much.
I use smugmug as well. GREAT site. For backing up files, I use mozy.com, and I can't say enought good things about them. Their software is very light and unobtrusive. They have a free service for 2GB, but I've upgraded, and it is still cheap for the 20 gigs or so I'm backing up. I've done several restores from backup, and it is always smooth and painless.
Ditto DropBox. Awesome way to sync important files across different computers, and I can access them even if I'm on someone else's computer. And if you all don't mind, I'll also share my referral...of course after someone has used Omer's. DropBox
http://Skydrive.live.com <- works with your current MSN id (hotmail, msn, etc.) I got 25GB to share stuff or host stuff.