There is such a wide variety of Joomla extensions available today that it is hard to determine and to sort through them all to find the most useful extensions to the core software program. Because of the software being open source, any third party can write an extension to the initial core components. This is why extensions to the Joomla software have flooded the market.
To make your job a little bit easier, we have weeded through the extremely large amount of extensions and narrowed it down into the most useful Joomla extensions that are available for you.
1. mtwMigrator. This is a component for the new v.1.5 version. It allows you to migrate all of your data from the old v.1.0 of the software to the new version. This software has made your job so much easier.
2. JoomlaXplorer. This program is an extension of the core components. It allows you to create new files and folders, upload content, search, move and delete files, downloads files, rename, copy, and so much more. It has definitely extended the Joomla core capabilities.
3 .JXtended Reports. This software will enable you to create and edit reports that pertain to your website. It is front end supported and will help you to keep track of visitor statistics and more.
4 .VirtueMart. This extension will allow you to turn your website into an eCommerce site. It can prove to become very valuable if you are going to operate an online store.
5 .JoomFish-Multilinguel Content Manager. If having control over the translation in your website matters to you, then this is the perfect extensions to you core Joomla software that will enable you to do such.
6. JCE. This is an advanced editor for WYS / WYG for the software program. Features include: plugin support, link and file handling, and more.
7.Joomla Pack. This is a Joomla back up component. This will help you to create a site back up that can be reinstated on any server that is adaptable to Joomla.
8. Core Design Login Module. This will help your site if you would like to control who has access to the site and who does not. It requires that the user enter a username and password before entering the site. Also has a link that the users will have access to just in case they forget their username and / or password.
There are so many extensions available and depending on what your individual needs are, will determine what extensions you will find extremely useful. It's hard to determine useful extensions without knowing what each individual person's needs are. This is just an "in general" list that will help you to get started.
Just remember that before installing absolutely unnecessary components, like the fun modules and plugins, you need to first extend the core components. If you don't, you could slow your website down to the point that it is unbearable for all who use it. So, choose your extensions in the proper order, then have fun. Your website can prove to be as unique as you are.