I connected to Google Play / Game Centre but my village isn’t loading!

The following is copied from the Supercell support page

First things first, please make sure you’re connecting to the right Google Play account. In lost village cases, it’s extremely important to use the correct credentials when logging in. If you can’t prompt your desired village with the email address you’re using now, that means it’s probably not the right one.

To properly access your village, please:

1) Make sure you have added the correct Google Play account to your Android device
2) In the in-game settings, tap on ‘Google+ Sign-in’ and connect with the e-mail address originally used to sync your village (the one you have lost)
3) If your village was linked to an old email that you no longer have access to, contact Google Support to recover your account’s information.

Supercell cannot access information related to your Google Play account, so we need the help of both you and Google to find the correct login details that will let you recover your village.

I connected to Game Center but my village isn’t loading!

First things first, please make sure you’re connecting to the right Game Center account. In lost village cases, it’s extremely important to use the correct credentials when logging in. If you can’t prompt your desired village with the email address you’re using now, that means you are not using the right one.

To properly access your village, please:

1) Login using the e-mail address originally used to sync your account
2) If it’s an old email, contact Apple Support to recover your account’s information.

Supercell cannot access information related to your Game Center account, so we need the help of both you and Apple to find the correct login details that will let you recover your village