Here's a list of suggestions compiled from various threads:
1. go to Settings -> Application manager -> ALL, find 'Google Play Store' and select it - Clear cache, if that doesn't work Clear data, if that doesn't work Force stop; if that doesn't work Uninstall updates (restart the phone between each intermediate step)
2. go to Settings -> Application manager -> ALL, find 'Google Services Framework' and select it - Clear data, if that doesn't work Force stop
3. go to Settings -> Application manager -> press the Menu button -> select 'Reset app preferences'
4. go to Settings -> Application manager -> ALL; scroll to the very bottom of the list and see if 'Downloads' is disabled - if it is, Enable it; also see if 'Google Account Manager' is disabled and if it is Enable it
5. go to Settings, find the Accounts group, select Google, select your Gmail address then select the 'Remove account' button. Restart the phone then add your Google account back.
6. Last is the dreaded Factory Reset - go to Settings -> Back up and reset -> Factory data reset. Be sure you've: synced your Google account; saved any pictures/videos to your computer or SD card or the cloud; saved any SMS/MMS that you care about (the Kies software is the only reliable method I've found to backup/restore MMS); saved your call logs if you care about that; backed up your application data if you want to save your game progress, etc.
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