Yes you can! Let's review all the options.
For Android and iOS devices
You can attach a Facebook account to your game profile in the game settings here:
After that, you'll be able to log in on any other mobile device by pressing "Save progress" button on the login screen.
Moreover, you can use the same Facebook profile to continue playing via PC or Mac! To do so, you'll need to go to Facebook Apps and log in using the very same Facebook profile.
For Web version
If you are playing via our official website, you'll need to press "Save progress" button on the login screen to attach an e-mail to your game profile.
After doing so, you'll be able to use that e-mail to log in the game on any other web browser or PC/Mac device. Just press the same "Save Progress" button again on other browser/device to get into your account.