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 listing displays modules specifically built to integrate with Drupal features. You can also browse directories of plugins or modules that are made specifically for Backdrop, Joomla and WordPress. The recommended way to add functionality to CiviCRM is using CiviCRM extension.

Allows you to display the CiviCRM menubar on non-civicrm pages of your website.
Aegir module to automatically setup Drupal instances with CiviCRM.
This module allows for users to access event payment receipts based on event contribution records in CiviCRM.

Receipts are created as Drupal nodes so site admins can enable printing/PDF exports.
CiviCRM and Drupal both place a copy of jQuery on the page, which is inefficient. This module removes Drupal's (older) copy and uses the single copy from CiviCRM for both applications. This results in faster page loads and a more responsive web browser.
Upgrades event iCal buttons to a better looking dropdown that includes a link to Google Calendar.