It’s always a good idea to encrypt your disks. That includes both your physical and virtual disks. Especially in a public cloud environment, you want to make sure that you encrypt your virtual disk files just in case someone might get access to those files. If the virtual disk files are encrypted, even if they’re stolen, no one will be able to access the information on the disks.
Azure IaaS services allow you to encrypt the virtual disk files using a feature they call Azure Disk Encryption. The service is relatively new, so it continues to evolve quickly. Microsoft recently released an update to their Azure Disk Encyrption White Paper, so if you’re interested in encrypting your Azure Virtual Machines, you might want to check it out.