Edit your view. and Under the "Advanced" settings of your Block details, click on
"Theme: Information". A list of options of template files will be displayed.
for example, if your block has a name "posts listing", see possible names listed by "Theme Information" option:
* Display output: views-view.tpl.php, views-view--posts-listing.tpl.php, views-view--default.tpl.php, views-view--block.tpl.php, views-view--posts-listing--block.tpl.php
* Style output: views-view-unformatted.tpl.php, views-view-unformatted--posts-listing.tpl.php, views-view-unformatted--default.tpl.php, views-view-unformatted--block.tpl.php, views-view-unformatted--posts-listing--block.tpl.php
* Row style output: views-view-fields.tpl.php, views-view-fields--posts-listing.tpl.php, views-view-fields--default.tpl.php, views-view-fields--block.tpl.php, views-view-fields--posts-listing--block.tpl.php
* Field Content: Title (ID: title): views-view-field.tpl.php, views-view-field--title.tpl.php, views-view-field--posts-listing.tpl.php, views-view-field--posts-listing--title.tpl.php, views-view-field--block.tpl.php, views-view-field--block--title.tpl.php, views-view-field--posts-listing--block.tpl.php, views-view-field--posts-listing--block--title.tpl.php
for example: your block has the name posts listing, and has style unformatted, then "Theme Information" suggest the name
views-view-unformatted--posts-listing--block.tpl.php (this is only one of several names). you can copy the original
views-view-unformatted.tpl.php template file (located in /modules/views/theme) to your current theme directory, and rename this file with the name suggested :
views-view-unformatted--posts-listing--block.tpl.php. then make the changes inside your template file. If this template does not allow make your wanted changes, seek other templates according your needs.
In the end, if you add a new template, rescan template files list:
Important! When adding, removing, or renaming template files, it is necessary to make Drupal aware of the changes by making it rescan the files on your system. By clicking "Rescan template Files" button you clear Drupal's theme registry and thereby trigger this rescanning process. The highlighted templates (in your template list above "Rescan template Files" button) will then reflect the new state of your system.
Also Theme Developer Module http://drupal.org/project/devel_themer suggested by Oswald could be useful to detect possible template/s to change specific elements according your criteria. I do not recomend this module enabled in productions enviroments (in my case, even I have disabled the module in test enviroments, because seems to have conflicts with views, but when it has been necessary, has been very useful)