modifying core block titles

If you want to do this in a way that is more easily portable, there are two possible approaches that I'm familiar with. Both will let you keep the changes out of the core or module so you don't have to worry about re-making them when you upgrade when a new Drupal or module release comes out. This can save you major headaches down the line.

1) use the locale module as described to substitute your preferred text:
http://drupal.org/node/24593
http://drupal.org/node/35037
http://drupal.org/node/58030

2) try doing this in your block template file. Here's an example for Drupal 4.7 that should work. This is a modification of the standard block.tpl.php that comes with blumarine or other templates for the phptemplate engine. It changes the name of the "Search" block to "Search site".

<?php if($block->module == 'search'): ?>

<div class="<?php print "block block-$block->module" ?>" id="<?php print "block-$block->module-$block->delta"; ?>">
  <div class="title"><h2>Search Site</h2></div>
  <div class="content"><?php print $block->content ?></div>
</div>

<?php else: ?>

<div class="<?php print "block block-$block->module" ?>" id="<?php print "block-$block->module-$block->delta"; ?>">
  <div class="title"><h2><?php print $block->subject ?></h2></div>
  <div class="content"><?php print $block->content ?></div>
</div>

<?php endif; ?>