If you’re going to rely on online storage, my recommendation is to pick one of the larger services, such as Dropbox, and even then I would also keep an additional backup on an external hard drive. Dropbox offers 2GB, with the possibility for more if you meet certain requirements. Like other services, Dropbox will sell you more storage if you need it. While nothing is guaranteed, Dropbox seem more likely to last than some of the smaller, less well-known photo storage sites.
If you’re interested in a Dropbox account and you don’t have one, please let me know, since I get an additional 500 MB storage for every friend who joins Dropbox.