Somewhere in your page.php template will be a tag containing the_title(), and that’s what you have to delete. In my WordPress theme, for example, the code looks like this:
<?php if ( have_posts() ) : ?>
<?php while ( have_posts() ) : the_post(); ?>
<div class="entry">
<div <?php post_class(); ?>>
<div class="post-meta">
<h1><?php the_title(); ?></h1>
That last line is the one you need to get rid of. You can simply delete it and the post title will be removed from all Pages.
Note: If you have a theme like Twenty Eleven that does not contain the <?php the_title(); ?> tag inside page.php, you’ll have to follow the clues from page.php to find out where the template is coming from. In the case of Twenty Eleven, page.php simply contains
<?php the_post(); ?>
<?php get_template_part( 'content', 'page' ); ?>
and no template tags at all. The clue is the get_template_part(): that tells us that page.php is pulling from a file called content-page.php. Look in the Twenty Eleven folder and you’ll find content-page.php there for your editing pleasure. And sure enough, it contains this line:
<h1 class="entry-title"><?php the_title(); ?></h1>
Delete that and you’re good to go.