Customise block.tpl.php

The default block.tpl.php resides at:

  modules/system/block.tpl.php

This can be copied and placed within the 'theme' directory. Afterwhich, this version will be used.

Customise block.tpl.php by block

To make specific to a particular block simply include the 'blockname' as follows: block-blockname.tpl.php.

e.g. block-views-news-block_1.tpl.php

Customise block.tpl.php by Region

To make specific to a region where the block is located simply include the 'region' as follows: block-region.tpl.php.

e.g. block-sidebar.tpl.php