Joomla is enough secure to be run across many servers on the internet, but securing it to the limit can be quite challenging.
It's a CMS used by many people so whenever a security hole is found, it's corrected by the Joomla team and a patch is released, so it's important to keep your Joomla website up-to-date.

We can ensure the Joomla security only by upgrading to the latest version, to protect it from exploit attacks.

It's important to know something about Joomla security, a must read is http://help.joomla.org/component/option,com_easyfaq/task,view/id,167/Itemid,268/.
This page talks about many Joomla-related security issues, like password length and .htaccess ffile configuration.

It's also advisable to subscribe to the security announces at the address
sicurezza http://forum.joomla.org/index.php/topic,40046.0.html

Be careful with installing thirty part extensions! They can cause a security hole in your system, if they're not well-coded.