http://support.google.com/googleplay/bin/answer.py?hl=en&answer=113410&topic=1046717&ctx=topic
Retrieving previously purchased applications
Your application purchases are tied to your Google Account and can be installed an unlimited amount of times on any device. So, for example, if you remove 'My Favorite Game' to save memory, you can reinstall it at a later date with no charge by simply visiting My Apps. Note: free applications are not saved to My Appsafter you remove them.
If you are being asked to purchase an application you have already purchased on Google Play on an existing or previous device, you might be using a different account than the one you were using at the time you made your purchase. Because the application is associated with a different Google Account, you are being charged to purchase it again. Additionally, if you are missing certain apps (free or paid), they might be registered under a different Google account. Fortunately, you can recover access to these apps by simply switching the account you’re currently signed into on Google Play.
The process to switch your account is dependant on the version of the Google Play Store app you’re currently using. You can find out which version of the Google Play Store app you’re using by going to Menu > SettingsApplications > Manage Applications > All, and selecting Play Store. The version is listed under the Play Store title. (On Android 2.1 or lower, you might need to select Menu > Filter > All to find the listing for the Google Play Store app)
To change the account you’re currently signed into on Google Play:
Google Play 3.0.20 or higherGoogle Play 2.3.06 or lower
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