I've always had the issue where I lose my data when switching from computers and it's always annoying to copy over data and paste it into the other computer just to play on the same world/have the same stats.

With the new Minecraft launcher released, I noticed you can now change the Minecraft directory and this is a great way to sync your data with Dropbox.

If you don't have a Dropbox account, I suggest you make one, not only for this but for syncing any data across devices.
You can sign up here, using my referral link: http://db.tt/bngDsQst (Using this referral link, I get a bonus at Dropbox)
If you don't wish to use my referral, you can sign up at: http://dropbox.com/ (Nobody gets bonuses and nobody is happy)

Now, you should install Dropbox from their website, that's easy and only takes a few seconds really.

Along with Dropbox, you will have to have Minecraft's new launcher. You can download it here: http://help.mojang.com/customer/portal/articles/1163345-new-minecraft-launcher

Now that you have Dropbox installed and the new launcher, it's time to set everything up. Open your Dropbox folder and create a new folder called 'Minecraft' (or whatever you want your game to be stored in)
Open the new Launcher, and choose release 1.5.2 from the dropdown menu for 'Use Version:'.
Now, check 'Game Directory'.
Copy the link to the new folder in your Dropbox account and paste it there. It should look something like this: (Assuming you are running on Windows)
C:UsersUSERNAMEDropboxMinecraft

Save the profile, log in and you're done. Now all your data is saved on Dropbox. :D