They are many extensions for Joomla! . Also every they new extensions are writing for custom use. But some of these extensions are very important. I like Joomla! because of its modularity. I used it many times and still I’m using in my projects. Let me try to list of my indispensable extensions.
1.JCE
JCE is a custom WYSIWYG editor. It is very easy and user friendly. There are a lot of features in it but two of them are very very important to me. First one is the show/hide button. I think all web-masters are like this feature. Second one is uploading images and import them to your content. Of course you can do this without JCE. But trust me it is easier 
2. VirtueMart
You need a cart or a catalog. So use this one. It is free and comes with many features. With this extension you can create a ready to use e-commerce site. Of course there are many CMS systems for e-commerce but as you may know joomla comes with many features.
3.Phoca Gallery
I like Phoca. This gallery is very easy to install and menage. It looks good and easy to custom. You can create categories and show them as menu items. Also you can call images or categories for your contents. If you need a gallery you have to look it first.
4.Akeeba Backup
Backup is a very important thing for all of us. Akeeba is a successful component for backup. I like this component but not for just backup. This tool is very successful about transport for your joomla site.
5. JoomFish
When I need to do a site with multi language function I have to use this component. I don’t think there is a substitution right now.
6.ChronoForms
Every body always needs some forms… This component is very easy to use and it is enough for simple form creation.
7.joomlaXplorer
Sometimes you don’t want use ftp or you cant. So this extension is a lifesaver at this times. You can upload, download and rename your files. I like this components when the customers don’t want to give their ftp accesses
8. sh404SEF
Every sites need seo… So you need this tool.
Sure there are many more lifesaver extensions for joomla! like kunena or SOBI2. But I don’t have to use this extension a lot. So I did not write thet to the list. But this is not mean I don’t like them or they are not good. The reason is they are so specific. If you are doing a directory SOBI2 is the way. Otherwise you don’t need it Thanks for reading and please comment your popular Joomla! Extensions.
powder on 
Keep up the fantastic piece of work, I read few posts on this website and I think that your web site is real interesting and has got sets of excellent information.
I am not sure where you are getting your information, but good topic. I needs to spend some time learning much more or understanding more. Thanks for fantastic info I was looking for this information for my mission.
it was greatly riveting to look over your blog, I want to reproduce your post in my blog. It can ? And you et an account on Twitter?
Keep up the good work, I read few posts on this website and I think that your blog is real interesting and contains sets of great information.
Pretty great post. I simply stumbled upon your weblog and wanted to mention that I have really enjoyed browsing your blog posts. After all I’ll be subscribing on your rss feed and I hope you write once more soon!
Wow! It’s a nice jQuery script; I was also exploring for that, therefore i got it right now from at this place. Keep it up admin.
Do you mind if I placed this blog post on my web site? I would give you credit and a link back to your blog. Thank you, and if possible let me know here, or email me!
Sure, you can do it