roberthq,
If you are using an older theme, it's probably using wp_list_pages to generate your nav menus. Two points:
1) It's actually the 'title' attribute, not the 'alt' attribute, that is causing the tooltip to pop up.
2) Filtering the output of wp_list_pages is quite difficult -- I know because I wrote a plugin that does it (but for a different reason).
For something like this, I would probably use JavaScript. Since your theme already has jQuery loaded, if you put this little piece of code in your template it should do the trick.
<script type='text/javascript'>
jQuery(document).ready(function($) {
$('#nav a').attr('title', '');
});
</script>
ekdor and PGrizz,
Something similar should work for you, assuming jQuery is loaded. You'll have to modify the CSS selector in the code to match your theme.