Imagebam is limited to JPG, GIF and PNG images and each file must be 4MB or smaller.
Bottom line, with 30+ GB of pictures and home movies, you could split the files among various free sites but you never know when any of those services will be discontinued. Particularly, if the photos and moves are not replaceable, I would recommend backing up to CD/DVDs or, probably a more practical solution as well as easier to use, a portable drive such as a Seagate Portable Drive.
Corrine listed some good options Here are a few more to think about.
Flickr - recently redesigned, now offers 1TB, yes 1 Terabyte of free storage. I think this would be the best option - Welcome to Flickr - Photo Sharing. However, photos only.