There are thousands of plugins and themes you can use to extend WordPress. You’ll find most of them in the official plugin repository at wordpress.org/extend/.
Editing: Inline, Rich Text, Reusable Content, and Attachments
Front End Editor and Inline Editor allow posts and pages to be edited without having to enter the dashboard.
TinyMCE Advanced allows you to add a number of buttons to the rich text editor, including a complete set of table buttons.
MCE Table Buttons is a simpler plugin that adds a row of table buttons to the rich text editor.
Post Snippets and Reusables allow you to define bits of reusable content that can be included in a post via shortcode and/or rich text editor buttons.
List Child Attachments (code.google.com/p/list-child-attachments/) provides a template tag and shortcode that lists all the files attached to a post or page.
Gallery Metabox shows a meta box on the post editing screen with a quick preview of the images attached to the post.
PJW MIME Config lets you configure the types of files that users (other than administrators) are allowed to upload to the media library.
Revisionary allows users to revise a published post or page without immediately publishing the change. Instead, the updates are submitted to an editor or administrator for approval.
Revision Control allows you to limit the number of revisions WordPress will keep. The site-wide setting can be overridden for individual posts.
Advanced Excerpt modifies the_excerpt() tag. It allows you to preserve HTML in excerpts, define the excerpt length, and change the ellipsis character.
the_excerpt Reloaded (robsnotebook.com/the-excerpt-reloaded/) provides a new template tag for excerpts. You can preserve specified HTML tags in excerpts, define the excerpt length, and choose what ‘more…’ text to display.
PJW Page Excerpt provides the excerpt box on page write/edit screens and allows you to use the_excerpt() for pages.
Custom Post Types, Taxonomies, and Fields
Custom Post Type UI provides an options page that allows you to create and manage both custom post types and custom taxonomies.
Convert Post Types and Post Type Switcher allow you to convert your old posts and pages to new content types.
More Fields and Advanced Custom Fields provide a simple user interface for creating meta boxes for custom fields.
Simple Page Ordering provides a simple drag-and-drop interface for rearranging the order of pages on any single level of the page hierarchy. A dropdown menu allows you to choose pages that have children and rearrange the pages on that level.
Hierarchy replaces the usual WordPress Edit menus with an outline-like overview of all your content, including all custom post types, and lets you dig deeper into each section from there.
Post/Page Lists & Navigation
Exclude Pages provides a checkbox on the edit page screen that allows you to explicitly include or exclude pages from WP’s page list functions.
Page Links To redirects posts or pages to another URL.
Yoast Breadcrumbs provides a template tag for breadcrumb navigation on both posts and pages. Pages display the page parents; posts display the category hierarchy.
WP-SNAP provides alphabetical listings of posts by title within a category.
Post2Post creates one-to-many or many-to-many relationships between posts (including pages and custom post types) and allows you to display the related posts in your theme.
Permalinks & Short URLs
Pretty Link turns your WordPress site into a URL shortening service of your own and can track visitors to the short links.
Jetpack includes wp.me, WordPress.com’s URL shortening service.
Workflow and E-mail Notifications
Subscribe to Comments allows visitors to receive e-mail notifications of follow-up comments on individual posts.
Subscribe2 allows registered users to receive e-mail notifications of new posts.
Clean Notifications reformats e-mail notifications in HTML, removing extraneous information and providing useful links.
Notifications to All Administrators sends all the common notifications to all users with the administrator role, not just the one whose e-mail address is shown under Settings à General.
Peter’s Collaboration E-mails sends a message when an author submits a post for review, and when a pending post is approved, scheduled, or changed back to a draft.
Editorial Calendar provides a calendar grid interface showing your scheduled posts.
Edit Flow includes an editorial calendar, configurable e-mail notifications, and new post statuses. It lets you create a more complex workflow for submitting and approving posts.
Contact Form 7 allows you to create e-mail contact forms with Akismet spam protection.
Gravity Forms (www.gravityforms.com) and Formidable Forms offer a great user interface, file uploads, e-mail autoresponders, and confirmation pages with data passed from the form input. Gravity allows user-submitted posts (with images, categories, etc.). Gravity Forms is a commercial plugin. Formidable is free with a limited feature set; the full feature set is available in the commercial Pro version.
Users, Permissions, and Login Screens
Members provides on/off toggles for all capabilities and allows you to define new roles. It also adds several features relating to private content.
Sidebar Login provides a login form widget.
Login Redirect allows you to reroute users (by username or by role) to a specified URL on login.
Registered Users Only requires users to log in before viewing your site.
Private Suite allows you to change the prefixes on private and password-protected post/page titles, set which roles can read private content, and create private categories.
User Contact Control lets you configure the contact fields on user profile pages.
Google Analyticator includes the Google Analytics code in your footer and provides checkboxes for advanced Analytics options, such as AdSense integration, tracking file downloads, outbound links, and admin visitors. It also adds a graph and some information about your most requested pages to your Dashboard.
Jetpack includes wordpress.com stats, which provides a graph of visitors and search queries as a dashboard widget.
Blubrry PowerPress provides extra fields for podcast and iTunes data, adds the necessary tags to your feeds, and displays media players for audio and video. It allows you to create separate podcasts from categories.
Jetpack includes a number of social media tools, including sharing buttons and a Twitter widget.
Twitter Tools provides a widget that will display your tweets as well as a number of advanced options such as autotweeting when you post to your blog, shortening URLs via bit.ly or other services, and adding a hashtag in tweets.
Sociable and Share This add a configurable row of buttons below your post that will allow users to quickly share your post with specified social networking services.
BuddyPress turns your WordPress site into a complete social network.
Events and Calendars
The Events Calendar allows you to create events (and optionally make a post for each) and display them as a small sidebar calendar, a large calendar in a post, or a sidebar list of upcoming events.
Events Made Easy lets you create events with location data and Google maps, RSVPs, with iCal and RSS feeds.
GigPress (gigpress.com) is designed for listing tour performances, but might work for general events. It includes microformats, RSS and iCal feeds, and CSV export.
WP Super Cache includes WP Cache and adds a number of other features: file locking, GZIP compression, cache rebuild options, and more.
W3 Total Cache uses APC or Memcached to cache database queries rather than files.
Batcache also uses Memcached and works on distributed servers.
WP Widget Cache speeds up page loads by caching widgets’ output.
Performance, Security, Maintenance, and Diagnostics
Better WP Security suggests changes to your site’s configuration to improve its security. It also includes a database backup tool.
Maintenance Mode displays a simple maintenance message to everyone except administrators.
WP-DB-Backup provides a button to quickly back up specified database tables and can be scheduled to back up to a specified directory.
Optimize DB performs MySQL’s automatic optimization routines on your database from the admin area.
P3 Plugin Profiler helps you identify performance problems.
Search & Replace allows you to replace text in chosen database fields.
Broken Link Checker runs a background process that periodically checks your site for broken links.
Show Template lets you know which theme file is being used to generate a particular page.
Hook Sniffer lets you see which actions and filters are involved (and in what order) as WordPress is generating a page.
Developer checks your installation for various development-related plugins and suggests others that might be helpful.
Debug Bar adds a debugging console to the admin bar.
Core Control lets you inspect several of WordPress’s internal processes, including filesystem access, HTTP requests, cron schedules, and upgrade routines.
WP Security Scan monitors file permissions, database security, and user passwords to help mitigate security vulnerabilities.
WordPress Firewall examines incoming requests and rejects those that match well-known attack vectors.
Login Lockdown and Login Security Solution allow you to limit failed login attempts.
WPtouch provides an iPhone app-style theme to mobile users.
Display Widgets allows you to display the widget’s contents selectively based on the page context, essentially providing a per-widget UI for the conditional functions.
Monster Widget adds all the built-in widgets to a sidebar in one click, allowing developers to set up widgets more quickly when testing themes.
Dashboard Notepad creates a Dashboard widget where you can store and share notes.
Search Engine Optimization
Google XML Sitemaps generates XML sitemaps (plain and/or gzipped) according to the sitemaps.org specification.
Yoast SEO and All in One SEO Pack reverses the order of the page/post and site names in titles, sets canonical URLs, generates metatags, and more.
HTML Import 2 imports HTML files as posts or pages.
CSV Importer imports posts from a comma-separated values file and can be used to import content from Excel.
Import Users from CSV allows you to add users in bulk.
Add Linked Images scans posts for image tags and imports the images to the media library.
See http://codex.wordpress.org/Importing_Content for many other import plugins.
Domain Mapping allows users to map their own domains to their network subdomains.
Proper Network Activation runs plugins’ activation routines on all network sites
Multi-Site allows you to create multiple networks from one WordPress installation. Each new network can have its own site administrator and subsites.