I recently started building my first serious Joomla site and I'm researching Joomla extensions which can help my site flourish.
Here are some of the Joomla extensions that I have installed at Top Bits.
Community Builder is one of the most popular Joomla extensions. In very simple terms, it allows members to build profiles on your web site.
Fireboard is a forum software for Joomla, very much like vBulletin
Joomla 1.5 SEOPatch
The Joomla 1.5 SEOPatch isn't technically an extension, but it does fix a lot of really glaring SEO deficiencies in Joomla. Hopefully this patch will be incorporated into future Joomla releases.
sh404SEF significantly improves Joomla's use of SEO friendly (and human friendly) URL's.
Joomap makes site maps for Joomla sites.
MultiAds allows you to integrate ads (such as AdSense) into your Joomla pages quickly and easily.
Add Keywords automatically adds meta keywords to every Joomla article you create. This only happens when you save the article, so be sure to install this extension before you start adding articles!
This Category displays a list of articles in a Joomla category. This helps point visitors to other content on your site and reduces your bounce rate.
FJ Related Articles Plus Module
FJ Related Articles Plus displays a list of related articles on your site. This helps point visitors to other content on your site and reduces your bounce rate. This list is generated using meta keywords, so be sure to install the Add Keyword extension first.
... more to come ...