Globals will be secure if you:
1. Work with register_globals=off which prevents submitted variables from being turned into globals.
OR
2. Make sure that ALL globals that you use are properly initialized. In other words, don't just do something like
if ($logged_in)
{
// Whatever
}
And assume that your code is setting the value of $logged_in. Initialize it up front.
Also, keep in mind that globals can make it harder to maintain your programs. It's sometimes difficult to figure out where they are being set.