You can find official Joomla resource information at Joomla.org.
Joomla Extensions Directory
At the JED, or Joomla Extensions Directory you can find 1000s and 1000s of extensions that add functionality to your site. From store front e-commerce solutions to photo galleries, the JED has a lot to offer.
I always recommend checking for exploits on an extension before using it. There are several places such as JoomlaExploit.com or the Vulnerable Extensions List at Joomla.org.
Favorite Extensions
- Slideshow CK
A responsive slideshow modules. Maximenu CK Mobile is needed in conjunction with the module for mobile optimization features.
- Maximenu CK
A versatile responsive menu with lots of features.
- Phoca Gallery
A very versatile and feature-rich image gallery component. Includes functionality for user uploaded images.
- Akeeba Backup
The most popular full site and database backup system available.
- Advanced Module Manager
Advanced admin features when working with modules. Allows many more options for module placement.
- VirtueMart
The most popular and versatile e-commerce solution for Joomla.
- Community Builder
Turns your site into a full featured social network. Very developer friendly.
- JomSocial
Another solution for a social networking website.
- Custom HTML Advanced
Custom code module for using PHP, Javascript, IFrames, and other codes.
- ChronoForms
A feature-rich forms creation and management component. Many actions available including the ability to charge upon form completion (paypal).
- XMap
Dynamic sitemap creation and management tool.
- Kunena
A very nice looking forum component.
- Events Manager
A very comprehensive events manager component.
- JEvents
An events calendar.