Is mysql auto increment safe to use as userID?

I am working on website that allows people to create profiles online. I was wondering if it is the right choice to use MySQL AUTO_INCREMENTed IDs as my user ids. Also bearing in mind that I might have to duplicate the database across multiple servers one day?

e.g. would you use this method for userIds on a website like Twitter or Facebook?

I have tried generating userIds with PHP before. I used something like this:

function generateID() {
      $possible = "1234567890";
      $code = "";
      $characters = mt_rand(7,14);
      $i = 0;
      while ($i < $characters) { 
            $code .= substr($possible, mt_rand(0, strlen($possible)-1), 1);
            $i++;
      }
      return $code;
}

This gave the type of values I needed, but I always had to check from the DB if that ID does not exist yet.

Isn't there a better approach?