Joomla definitely improved module management, but it still does not have the power that AMM brings to the table. Not only can you control when and who sees a particular module, one of the most useful features is the ability to color code the modules. Once you try it you will wonder how you ever lived without it.
2. ACL Manager
This is one of the pure few commercial extensions, but it is worth every penny of the 10€ the developer charges for it. While a much needed addition to the core, the Joomla ACL is rather difficult to navigate. Particularly since managing the ACL tends to be a set it and forget it function, I always found myself digging around trying to find a particular permission. ACL Manager fixes that with a simple one page interface. All of the permissions for everything in one nice grid that can be filtered by user, group, or extension. This extension is worth much more than the price, it really should be included in the core. It's that good.
What Joomla must have list would be complete without JCE? The de facto WYSIWYG editor for Joomla for several years now, it just keeps getting better. It has a fantastic media manager and link manager and a ton of plugins to integrate many popular extensions. It does a very good job of creating clean code and the Paste as Plain Text option is a life saver for Microsoft Office users.
Over the last couple of years I've tested most every CCK made for Joomla. There are some that are more powerful, some that have fancier interfaces, but none that combine easy management and powerful modifications quite like K2. Out of the box the included features make it a great replacement for com_content, even if you don't need the custom content features. The media, image, attachment, and comment features make it just about the perfect addition to any content heavy site. We are so impressed with K2 that the majority of the extensions we've contributes to the Joomla Extension Directory are K2 specific.
Another long standing top Joomla extension, ChronoForms in another user friendly yet powerful tool in the Joomla toolbox. Simple enough for even the least tech savvy user to create rather complex forms with little trouble. The new event based advance wizard editor allows for extensive modification and customization to any form. The form action system gives an even greater flexibility to integrate with just about any extension or third part API. In the hands of an experienced programmer it can actually be used to create full blown applications.
What can I say about Akeeba that hasn't been said before? This extension isn't just part of our core install, it's how we install every site we build. Akeeba makes backing up so simple there is no excuse for not having a current backup. Spend a few dollars to get the pro version and you can even schedule and store backups on several popular cloud storage solutions.
Honorable Mention - RS SEO Suite
This extension is a new one to BNR, but RS Joomla has been around for a while. While it doesn't do the work for you, it makes keeping track of your SEO efforts a breeze. It has a very easy to understand interface that will basically walk you through the optimization process to insure that you are getting the most bang for your buck on each page. It also has a powerful sitemap tool and Google Analytics integration. So far we're impressed, so much so that we've upgraded to an unlimited license for use on all of our sites. Even if you hire an SEO firm to do the work for you, this tool would be invaluable to help you track the changes being made on site.
So there you have it. There are other fantastic extensions that we use, but this is the core of every install we do. Think we missed a good one? Tell us in the comments.