There is a fast, safe and easy way to upgrade multiple blogs using SVN. First, you have to install WordPress by following the instructions here.
Upgrading through SVN saves you from downloading and extracting a ZIP file manually, and if you made modifications to some files (mostly workarounds to stupid PHP bugs), they are kept.

Then just use this script:

set -u
LASTVERSION="2.3.3"
for WP_VER in "lolcats.domain.tld" "ronpaul2008.domain.tld"
do
    cd "${HOME}/www/${WP_VER}/" || exit 1
    svn sw "http://svn.automattic.com/wordpress/tags/${LASTVERSION}/" || exit 1
    lynx -dump "http://${WP_VER}/wp-admin/upgrade.php" || exit 1
    sleep 5
done

Obviously you need SSH access. If you don’t have SSH access, most likely on shared hosting, switch hosts. Nobody can live without SSH.