Extensions are installable packages which give CiviCRM new functionality, and this directory provides a centralized list of extensions which the CiviCRM community has created.

Further resources:

This extension makes it easy to have all email sent from Outlook stored on the appropriate contacts' records as Email Activities in CiviCRM. Code in Outlook talks directly to CiviCRM native APIs. The next version of the integration (hopefully out early fall 2015) will integrate Outlook Calendar with CiviCRM....
Current Usage: 140
This extension tries to make public bank data like name, BIC code, and national bank ID accessible for CiviCRM. The information itself will be downloaded from the various national sources, and can be updated any time. The information will be stored in a new option group....
Current Usage: 138
Store documents on the contact dashboard A document can be linked to more than one contact Version management with a document Custom search to find documents  ...
Current Usage: 138
When people sign up for an event, you may want to offer registration for an additional event or membership dues while they're checking out.  This extension ties event registration or membership to a price option, so you have full control over the price--potentially offering a discounted bundle rate....
Current Usage: 137
Membership Extras for CiviCRM
Current Usage: 132
Provides email delivery for email from CiviCRM via MailChimp's Mandrill service.
Current Usage: 132
“Simple Donate” extension which allows the administrator to link existing donation pages with our new sleek, user friendly and responsive donation page....
Current Usage: 126
This extension provides additional mail merge tokens for CiviCRM that pull in CMS content....
Current Usage: 122
With the data processor you can build complex queries easily in the user interface and display them as a search, api or export as CSV.
Current Usage: 120
Recording contacts' gender in a database in an inclusive way can be tricky. On one hand, you don't want to put people in a box. The ideal input on a form would be a free-text field like: My gender is: ______. On the other hand, you want your data to be searchable and sortable, and free-text input from users is not good for this. This extension gives you the best of both....
Current Usage: 120
The CiviCalendar extension is an CiviCRM component which allows visualizing different types of cases, events and activities.
Current Usage: 118
This is a CiviCRM extension designed for large scale donation receipt generation in a heavily regulated environment (e.g Germany).
Current Usage: 118
This civicrm extension allows an anonymous user to have an autocomplete field instead of a free form one for the current employer, to avoid mispelled/duplicate organisation names Tested on the following forms:...
Current Usage: 115
Action Provider is an extension which provides action to other extensions. Such as Form processor and the Search action provider.
Current Usage: 115
This extension changes the default so it doesn't send a confirmation email when registering a contact to an event from the back office. Nothing more,  really simple but avoids sending emails by mistake....
Current Usage: 107