For disk-image backups I've used
PING (Ping Is Not Ghost) and like it. They do ask for an email address before downloading - which is annoying - but I've never had any spam from them. In theory it's not doing anything you couldn't do yourself with a Linux LiveCD (the guts of it is partimage) but it's already packaged for you. You'd want to use it with something like GParted to do the resizing after a restore.
For file backups I use the Win7 Backup tool. I used to use
Areca which I liked because it was cross-platform. It also has a feature I liked where it would consolidate old incremental backups. However I found that as nice as that sounded in theory it took a lot of time to perform and since I rarely used it I eventually stopped using it. But I'm talking about my work PC here and since my job changed very little of what's on there that's important isn't backed up somehow anyway, and for that I can store stuff on a network drive that is.
At home I use BackInTime - which is an rsync frontend. It's trying to be a sort of Time machine for Linux and it's OK. I have had some issues with restoring files - I've found the GUI performs horrendously slowly with lots of files, so I wrote a little script for that. I do back up and restore semi-regularly as I use Mint where the standard upgrade advice is to back up your files and do a new install.
I tried Crashplan and liked it - simple to set up, free version is still very useful, cross-platform - my one qualm is that the backups are in some proprietary format. For file-based backups I like something I can go in and just grab the files individually if necessary.