Observer.php

<?php

class Companyname_Sendmailregister_Model_Observer
{
    public function customerRegisterSuccess(Varien_Event_Observer $observer)
    {


    $customer = Mage::getModel('customer/customer')->load($observer->getCustomer()->getId());


    if(!empty($customer))
                {
                    $mailTemplate = Mage::getModel('core/email_template');
                    /* @var $mailTemplate Mage_Core_Model_Email_Template */

                    $translate  = Mage::getSingleton('core/translate');

                    $templateId = 1; //template for sending customer data
                    $template_collection =  $mailTemplate->load($templateId);
                    $template_data = $template_collection->getData();
                    if(!empty($template_data))
                    {
                        $templateId = $template_data['template_id'];
                        $mailSubject = $template_data['template_subject'];

                        //fetch sender data from Adminend > System > Configuration > Store Email Addresses > General Contact
                        $from_email = Mage::getStoreConfig('trans_email/ident_general/email'); //fetch sender email
                        $from_name = Mage::getStoreConfig('trans_email/ident_general/name'); //fetch sender name

                        $sender = array('name'  => $from_name,
                                        'email' => $from_email);

                        $vars = array('customer'=>$customer); //for replacing the variables in email with data
                        /*This is optional*/
                        $storeId = Mage::app()->getStore()->getId();
                        $model = $mailTemplate->setReplyTo($sender['email'])->setTemplateSubject($mailSubject);
                        $email = $customer->getEmail();
                        $name = $customer->getName();

                       $model->sendTransactional($templateId, $sender, $from_email, $name, $vars, $storeId);
                        if (!$mailTemplate->getSentSuccess()) {
                                throw new Exception();
                        }
                        $translate->setTranslateInline(true);
                    }
                }



    }
   public function customerRegisterSuccessCheckout(Varien_Event_Observer $observer){

    $customer = Mage::getModel('customer/customer')->load($observer->getCustomer()->getId());

    //if (!$observer->getCustomer()->getOrigData()) {

    //$customer = $observer->getEvent()->getCustomer();
   // if (!$customer->getId())
     //   return $this;

   // if(Mage::registry('customer_save_observer_executed_'.$customer->getId()))
   //     return $this;


       if (Mage::registry('if_observer_already')) {
        return $this;
    }

    Mage::register('if_observer_already', true);

    if (!$observer->getCustomer()->getOrigData()) {

      if(!empty($customer))
                {
                    $mailTemplate = Mage::getModel('core/email_template');
                    /* @var $mailTemplate Mage_Core_Model_Email_Template */

                    $translate  = Mage::getSingleton('core/translate');

                    $templateId = 1; //template for sending customer data
                    $template_collection =  $mailTemplate->load($templateId);
                    $template_data = $template_collection->getData();
                    if(!empty($template_data))
                    {
                        $templateId = $template_data['template_id'];
                        $mailSubject = $template_data['template_subject'];

                        //fetch sender data from Adminend > System > Configuration > Store Email Addresses > General Contact
                        $from_email = Mage::getStoreConfig('trans_email/ident_general/email'); //fetch sender email
                        $from_name = Mage::getStoreConfig('trans_email/ident_general/name'); //fetch sender name

                        $sender = array('name'  => $from_name,
                                        'email' => $from_email);

                        $vars = array('customer'=>$customer); //for replacing the variables in email with data
                        /*This is optional*/
                        $storeId = Mage::app()->getStore()->getId();
                        $model = $mailTemplate->setReplyTo($sender['email'])->setTemplateSubject($mailSubject);
                        $email = $customer->getEmail();
                        $name = $customer->getName();

                       $model->sendTransactional($templateId, $sender, $from_email, $name, $vars, $storeId);
                        if (!$mailTemplate->getSentSuccess()) {
                                throw new Exception();
                        }
                        $translate->setTranslateInline(true);
                    }
                }

    //Mage::register('customer_save_observer_executed_'.$customer->getId(),true);
        }

   }
}

?>