New Kind of Device
Many of the app stores have a way to restore your purchases with out an additional charge. However, if you move to a new device that does not come with the same app store as your last device, you may need to purchase again. For example, if you move from Android to iPhone, a second purchase will be necessary.
Same Kind of Device
If you didn’t switch platforms, you can likely restore your apps without an additional purchase because your software is probably safe with your account, or backed up on your computer. Read these articles for more information:
iPhone, iPod Touch, and iPad
Google Play & Android™ Devices
Amazon Appstore and Kindle Fire or Fire Phone Devices
NOOK, Restore Apps from the Cloud
Learn about your Library – Be careful not to delete an app! Move it to your Cloud instead.