Some Joomla! extensions you always use, some you only install when the situation asks for it. There are paid extensions and free, open source extensions. In most cases, you will be able to find the functionality you are looking for amongst the many free extensions in the Joomla! extensions library.
After a fresh install of Joomla! 1.5, I start adding my favorite extensions to the install. These are the extensions I use for each and every install, although I might run into an extension later I want to add to my main extensions list. In another post I will explain how you can install extensions into your Joomla! install.
My Favorite Joomla! Extensions
All of the extensions below will be explained in more detail later in the Extensions category on this blog, and will be linked to from this page. The extension name itself is linked to the extension’s page in the Joomla! extensions library.
sh404SEF
Joomla!’s URLs don’t look too good directly out of the box. You can select them to be more search engine friendly (SEF), but sh404SEF does the job a whole lot better. This extension is commercial nowadays, but it is worth the investment. I still use the free version, though.
JCE
The built-in editor in every Joomla! install is called TinyMCE. TinyMCE is workable, but when you want to have a decent editor with a lot more options and possibilities, look no further than JCE.
There are a lot of extensions for JCE specifically (make sure to install the free JCE Utilities from JCE itself), so you can modify the editor to your liking.
JoomlaPack
Every website needs to be backed up, and JoomlaPack is the best for Joomla! websites. It also creates backups with an automatic installer, so you can prepare your site, back it up and install it in its final location.
Xmap
No website is complete without a site map, and Xmap creates them on the fly whenever the site is updated.
BIGSHOT Google Analytics
As a savvy webmaster, you will want to have a deeper insight in your traffic. Google Analytics provides that – for free – and BIGSHOT Google Analytics places it on your Joomla! pages easily.
SEO Simple
Joomla! does not give you the possibility to add meta tags to your section and category pages. SEO Simple automatically takes the first part of the text on your page and adds that to the page as a description tag.
Language Pack
When you’re building sites in another language than English, you will want to change the site’s frontend and – maybe – backend to the desired language. There are translations in loads of languages available via the link.
JForms
To build contact forms, JForms is the best! I tried several others, and – even though it has its flaws – I stopped at JForms.
JComments
The best way to keep visitors coming back is by allowing them to participate on your site. JComments does the best job here.
Ninja RSS Syndicator
This extension allows you to create custom RSS feeds for each and every section and category combination you want.
AddThis
When you want your visitors to list your site on social bookmarking sites, this extension gives them that opportunity straight from your site.
Banner Slider
I was looking to add banners to my site, but wanted to have them change during a visitor’s stay. Banner Slider provides an easy way of showing multiple banners in one spot where you want them to show up.
Front-end Font Size Adjuster
To facilitate the seniors and people with poor eye vision, it is great to enable them to increase or decrease the font size used on your site. This extension is the best I found.
Missing Metadata
When you create a lot of content, you will definitely sometimes forget to add the necessary metadata to an article. This extension shows you which articles’ meta data fields have not been filled.
MultiAds
To place Google Adsense ads (or any other types of ads) on your articles, MultiAds is the easiest and most versatile solution.
Simple RSS Feed Reader
I make use of many RSS feeds on my sites to give the visitors fresh content regularly. This extension does a great job doing that.
Phew! That was it! These are the main extensions I use on my sites. In future posts, I will explain the details of each extension, plus how you can best put them to use.
_____________________________________________________________________________________________Robin Roelofsen
"I think complexity is mostly sort of crummy stuff that is there because it's too expensive to change the interface."
Jaron Lanier

Nice list, a lot of great extensions.
Thanks! I listed the main ones I use when setting up a Joomla! site. Of course, there are more I use mostly in specific cases. I plan on expanding on all of them soon!