I work with several different computers on a daily basis and sometimes it can be a chore to keep up with multiple copies of files and remember which machine has a particular file. In particular, I have a few applications that are constantly out of sync with one another and manually keeping them in sync is next to impossible. With the release of Microsoft Live Mesh, I have been able to solve the problem (at least to some extent). I'll show you how.
Password Managers
It's a good idea to use different passwords for each site, but this is not easy to accomplish if you don't have a password database at hand. My password manager of choice is KeePass. With this free/open-source application, you can store your secrets in an AES encrypted file. However, if you need to access your passwords on multiple computers, you are out of luck. That is, unless you use Live Mesh. If you store your password database in a Live Mesh folder, it will stay synchronized amongst your various Live Mesh devices.
Please note that there is one very important thing to be aware of if you decide to do this. Storing all of your passwords or anything of sensitive nature inside of a product labeled as "TECH PREVIEW" is not safe. If you are going to do this, it is highly recommended that you take advantage of the two-factor authentication that KeePass provides. Using this option will require a key file in addition to a master password. The password database will be useless without these two pieces of information. The key file will need to be present on each computer that opens the password database. Oh, and by the way, don't store or even transmit your key file to your other computers using Mesh, that would be defeat the purpose of using two-factor authentication.
TODO List
My friend Chris Craft showed me this free application years ago and I have recently started using it again. It's called ToDoList by AbstractSpoon. I use this application to keep up with my various tasks. As I make changes to my task list on one computer, my most recent task list will be waiting for me at my other computers whenever I open the application. Of course, there are other ways to maintain a centralized task list, but this is just another option. By the way, it's free.
Conclusion
These are just two simple cases that I have found to be helpful in my daily routine. I'm certain that there are many other applications that which could benefit from Live Mesh as well. I'd be interested to hear about any other interesting uses you may have found for this technology!