The update.php doesn't want to run it's complete course I updated core Drupal (D7.14) and all seems to running perfectly. Only some updates for the database are required. So I run the update.php and I get through the first stages and I can see the pending updates when I am on the Review updates page. But when I continue (press the button). It seems to get stuck. I don't get to next screen, it just keeps on loading. In one browser I get a blank screen but that's it.
Happened to me too. One update took a lot of memory on my shared host. I tried it several times during the Day until I got Lucky.  Maybe a glance in the Apache log Files will help?