field--field_image.tpl.php
file into your theme folder and then comment the following 3 lines (Lines 26-29):
<?php if ($node->field_image[$lang][0]['alt']) :?> <p><?php print $node->field_image[$lang][0]['alt']; ?></p> <?php endif; ?>
If, for example, you want to apply this change only to the Blog content type, please duplicate the
field--field_image.tpl.php
file, then rename it to
field--field_image--blog.tpl.php
and, finally, make the above-mentioned change.