There are thousands of Joomla extensions. Even if an extension is well programmed, it may not fit your needs. Some extensions are more versatile than others and to hopefully save you a lot of work in terms of installation and testing and subsequent uninstallation, we've created this little informal list of good and versatile extensions that most people will have much benefit from regardless of the purpose with sim Joomla installation.
Akeeba backup. Excellent backup tool installed and used in the backend of your Joomla installation. Is a free "must have" extensions.
Joomla Watch. Great stats tool that logs all visits to your Joola side. Stores where visitors come from and what keywords on the search engines that lead them to your site. Available in both free version and a current pro version.
VirtueMart. A proven and complete e-commerce solution. To this extension there are many additional expansion. Extensions to extensions in other words.
Kunena. The most widely used forum solution for Joomla. Let the users themselves create content for your website. With all the features you expect from a forum solution.