If you want to customize the block.tpl.php for different blocks. The Block Theme module could serve this purpose well.
1. Download and enable the module.
2. Go to the Block Theme configuration page and create the template name pair as follow.
3. Then we need to create the block--blocktheme--eureka.tpl.php. I am using the Omega theme so i copy the block.tpl.php from the Omega core to my Omega starter theme folder and rename it to block--blocktheme--eureka.tpl.php.
4. Customize the block--blocktheme--eureka.tpl.php. In this example, i will add a hello world greeting before the block content.
5. Go the your block configuration page where you could select the Block Theme.
6. Save the block and check it out.
Reference: Drupal Module – Block Theme