This is by far the most useful extension that you will ever install on your site, ever. As far as I am aware no other extension for any CMS (Drupal and WordPress included) comes even close to offering the restore and backup capabilities that Akeeba provides for Joomla!. Akeeba lets you backup, compress and restore your site with all it’s files and database, even large sites, within minutes. Its also a great way to migrate sites between servers or accounts with minimal effort.
2. Extplorer
Extplorer allows you to access all your site files through an easy to use browser interface without having to login to Cpanel or go through a local FTP client. It installs as a simple component in Joomla!. It can be used to make updates to PHP code, HTML and CSS directly in the browser. This is a must have for developers who often need to make changes to template files while also working directly in the Joomla! backend. It can also be used to bypass the native Joomla! media manager to upload and rename files and folders, a useful tool given the limited nature of the media manager.
3. Roksprocket
If you need a way to display your Joomla! content through a module Roksprocket is hands down the most versatile and best extension for this purpose. It has the ability to display and filter articles in the form of highly configurable sliders, tabs, mosaics and more. It also lets you define your own custom content and has built in K2 support. One good thing is that the function and design of the module is really good out-of-the-box so little time needs to be spent on customizing it.
4. JCE Editor
Lets face it. The default TinyMCE editor that comes prepackage with Joomla! leaves much to be desired. JCE editor provides and instant upgrade to your WYSIWYG. It integrates with the Joomla! ACL so that you can give your authors and editors different functionality based on thier permissions. It also has a powerful file upload and managment system. In particular the image manager is a very useful tool which allows you to make minor edits to images on the fly.
5. K2
K2 provides a wide array of additional functionality and fields to Joomla!’s category and article system to supercharge your site. A review and comment system are some of the add-ons you get, plus additional multiimedia fields for embedding images and videos.