Bitcasa starts you off with 10GB for free, but $100/yr throws the floodgates open and gets you unlimited storage for anything you want to sync, share, or back up. Plus, you can connect as many computers or devices to your account as you choose, so you don't pay by the PC. It's client isn't quite as robust as some of the other tools here, but if you're more interested in a flat fee for unlimited space and you can handle the details of which files go where and when, it's a solid option. You can read more about Bitcasa's pricing here.
For this software, you just need to copy the YouTube link and paste it directly into the box that’s labeled for the link. Then you get to choose the format that you want to download it into. You’re going to need to download their specific software in order to be able to download, but then you just have to click to download, and you’re all set. It really is just that easy. You can even tell it to download multiple URLs at the same time, so you can fill in everything you want to download and tell it to start while you head off to do other things.