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:

Geocoder extension provides geocoding from multiple providers (default is Open Street Maps) with advanced features over core geocoding Requires - CiviCRM 5.x, php 5.6 Credit : the Wikimedia Foundation
Current Usage: 173
You like how tags are displayed in the contact summary? this extension does the same, for relationships.    ...
Current Usage: 162
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: 158
Allows adding an automatically calculated "Additional Percentage" field to any price set (e.g., add 3% to cover credit card fees).
Current Usage: 154
What is CiviBooking? Are you a non profit with Rooms or Resources that you think you could raise money by renting out? Or are you a community center or voluntary service looking to manage your resources better? Sick of spreadsheets, emails and that Google calendar that no one keeps up to date? Then CiviBooking is the extension for you!...
Current Usage: 150
A tool that allows you to easily correct invalid phone numbers.
Current Usage: 146
Multisite (url) based permissioning.   This is a port of the drupal multisite module to an extension. It allows the CiviCRM multisite concept to be extended such that the site a contact logs onto will affect which contacts they can see and edit....
Current Usage: 142
The CiviCase v5 extension is an overhaul of the CiviCase UI. It provides a richer experience with more thoughtful layouts and interactions.
Current Usage: 142
SYSTOPIA OpenStreetMap CiviCRM Geocoder This CiviCRM extension adds the Nominatim OpenStreetMap server as a geocoding option. Just install the extension, and activate via "Administer" => "System Settings" => "Mapping and Geocoding"....
Current Usage: 139
PDF API for CiviCRM to create a PDF file and send it to a specified e-mail address. This is usefull for automatic generation of letters The entity for the PDF API is Pdf and the action is Create. Parameters for the api are specified below:...
Current Usage: 131
“Simple Donate” extension which allows the administrator to link existing donation pages with our new sleek, user friendly and responsive donation page....
Current Usage: 131
Automatically corrects email addresses when they're added, and allows for mass correction. Rules can be configured.
Current Usage: 127
Places recently-viewed items in the Menu bar for quick access.
Current Usage: 125
Onscreen tutorials for learning to use CiviCRM
Current Usage: 125
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: 122