Every developer who works with Joomla has their own favorite, must have, extensions. These are mine. :)
JomSocial is a social publishing platform for Joomla. You can customize profile fields, Create groups, Invite friends, Send private messages, Comment on walls, Share photos, Follow updates via activity stream and Integrate 3rd party components with API. So far I love this extension but it is very new so there aren’t very many third party applications yet. It is gaining popularity very quickly.
JCE TinyMCE on steroids. Have more to your WYSIWYG Editor. A lot of features and a great way to configure them. Plugin management and many more. Maybe sometimes to many.. An advanced, configurable WYSIWYG editor for Joomla! based on Moxiecode's TinyMCE. Includes advanced Image/Media and File handling, plugin support, and an Administration interface for editor configuration. This is the first extension I install on every Joomla project.
JCrawler is an open-source (under the CPL) Stress-Testing Tool for web-applications. It comes with the crawling/exploratory feature. You can give JCrawler a set of starting URLs and it will begin crawling from that point onwards, going through any URLs it can find on its way and generating load on the web application. The load parameters (hits/sec) are configurable.
DOCman is an open source Document Management System (DMS) for Joomla!TM 1.0 and 1.5. With this component you can manage documents across multiple categories and subcategories and give users permission to upload, download or edit documents. This extension works in the front end and can help you track which files are being downloaded.
I love this module because it is a fully customizable login module. SignalLogin is a Module, that is built to provide a more versatile way to show your Login-Forms. Along with various configurable Options, you can fully customize it's looks and switch between horizontal (i.E. Mini-Login-Bar at the top of your Page) or vertical (i.E. full Module in Sidecolumn). Just released: The Joomla 1.5-Version, featuring all the Bells and Whistles of J!1.5, such as Encrypted (https) Logins, Pulldowns to choose Login- and Logout-Redirection, Multilanguage etc. paired with SignalLogin's great Look and Flexibility!
WowJoomla's LightBox Login/Register
This Module not just saves on valuable real estate for your site but gives you a slick web 2.0 login box using a modal lightbox script. I love it and my clients love it.
This powerfull Joomla module allows you to display CSS dropdown menus (AKA Suckerfish). There are a handful of CSS drop down menus available to Joomla, I typically prefer this one over others due to its raw power and functionality. If you are somewhat of a Joomla novice, I do not recommend this module as it tends to be difficult to setup if you are unfamiliar with CSS. If you are a developer, this module will offer you a solid base in which to build a totally customizable menu system that fully integrates with existing Joomla menus.
No eCommerce site should be without a virtuemart installation. This component provides an out of the box shop. An extensive plugin API allowed the component to grow into a full ecommerce solution. There are now a huge amount of payment plugins available for virtueamart, and there are lots of freelancers able to build you a custom made one (if you have some exotic payment processor). Products and Manufacturers can be very easy setup, and shipment costs can be customized with ease. After trying Virtuemart there are not enough horses in the world to drag you back to OSCommerce
Chrono Forms is not one of these easy to use if you don’t know how to code kind of extensions, which is exactly why I love it, it’s by far the most flexible and feature packed form management extention I have used.