I've been playing with a few cool tools/services of late: foldershare (free) to sync files between computers over the net (sort've private p2p file sharing), mydatabus for free web-based online storage/backup (free up to 5GB!) - allows public file serving as well. And finally jungledisk, which uses Amazon's totally cool S3 service for online storage (pretty cheap at $0.15 per GB / mo) and appears like a mounted drive on all/any of your computers. And these all work on OSs other than Windows as well, which has gotta be good... Jungle disk is currently free but eventually going to cost a few dollars. All of this is great for saving off-site backups of those precious family photos, videos, documents etc. Oh, and you can encrypt them all for security with axcrypt, so nobody else can pry into your stuff! (Which is free, and open source!)
There are just tons of these kinds of services around, but these ones look like the cream of the crop to me. Although... I wonder if/when Google will come out with the much-rumoured "gdrive" (Project Platypus) which might do all this kind of thing in one package?
Update, April 07 - you can also interact more directly with S3 using free tools like jets3t or s3fox. Which can be very useful. And then with a bit of cunning with a new DNS CNAME you can use S3 to host public files for your website etc.