For example
1). I use dropbox and skydrive. It's more or less a backup, as the files are synced to my computers...so even if they lose it all, I still have it. In the event I lose it all, I have an offsite copy of my data.
2). gmail: no more do I have to bother with backing up a PST when I switch computers, and I can access 100% of my email from any device with a web browser. Downtime hasn't been an issue for me, gmail is extremely reliable.
3). google sync: I use Chrome and my bookmarks are all synced with my google account. No need to save any bookmarks, as they are in my account and conveniently on every single machine that I use, tablets included.
4). Amazon MP3. It took me a long time to move to digital music, but the prices have been good, and it's DRM free and you can download and re-download any song you want however often you want. If you are limited on storage space, you can stream from the cloud to your device. I can have up to 10 devices on my account, so I can keep music on my phone, my wife's phone, my computer, etc. And I download all of the music to my home file server, so in the event that Amazon decided to rip the rug out from under me, I still have all of my music.
Having access to my data no matter where I am is becoming more and more normal. Having an offsite copy of my data in the event of fire, theft or other disaster is certainly appealing. For things that are private, I use Box Cryptor, TrueCrypt or KeePass to store them...or a combination of technologies.