To remove validation for telephone number. You need to do three things.
Step 1:
remove client side validation for telephone input field.(remove validation class) In following files
checkout/onepage/shipping.phtml
checkout/onepage/billing.phtml persistent/checkout/onepage/billing.phtml
Step 2:
Need to remove validation from code side.
app/code/core/Mage/Customer/Model/Address/Abstract.php
Copy this file to local
app/code/local/Mage/Customer/Model/Address/Abstract.php
Then find a line
if (!Zend_Validate::is($this->getTelephone(), 'NotEmpty')) {
$this->addError(Mage::helper('customer')->__('Please enter the telephone number.'));
}
Comment the above lines to remove the validation from code side
Step 3:
Need to remove validation value from DB. For that follow @saravanvelu answer.
Refer this