This is the weirdest problem I have encountered. I am using mod_rewrite in .htaccess in Apache/2.2.13 (Linux/SUSE), and it appears to not be called when there is no trailing slash in the URL. I tested by putting garbage in the .htaccess file, and only received 500 errors when the trailing slash was added, but 404 when omitted. I honestly have no idea why.
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} -s [OR]
RewriteCond %{REQUEST_FILENAME} -l [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^.*$ - [NC,L]
RewriteRule ^.*$ index.php [NC,L]
/name fails with 404
/name/ is successful