Plugins are either small supplementary programs for the basic WordPress operation, or upgrades for its stock functions. They're easy to install and easy to turn on and off.
While most plugins just need to be activated to work, there are a few that need a small tweak made to some system file first, so check for docs or try the home site if something's amiss. And always glance over the 'Installation' page when downloading a plugin from the WordPress site.
Some plugins have settings on the 'Settings' page, and some need to be flipped on in their settings before they'll work. It's a good habit to check the 'Settings' page whenever you install a new plugin.
Some plugins work in the background and aren't normally accessed. Plugins that are actually run can be anywhere. The 'Tools' area is the most popular spot, but you'll find them throughout. Some of the 'global' ones place themselves in the Dashboard area, some of the theme-related plugins put themselves in the 'Appearance' area, plugin-related plugins might plop themselves in the 'Plugins' area, and some plugins will have the audacity to plunk themselves right on the tool bar.
CKEditor — the best of the second-party editors
WP-DBManager — backs up database, just in case
Exclude Pages — easy way to keep pages from displaying in the sidebar
Broken Link Checker — checks for broken links and lost pictures
Remember Me — keeps you permanently logged in
Better Comments Manager — more control over comments
Subscribe to Comments — notifies user when additional comments are left
Si Captcha — Used to prevent spamming
A whole bunch of comment-related plugins here
Dagon Secure Form Mailer — simple contact form
CForms — excellent full-range contact form w/skins
All In One SEO Pack — optimizes site for search engines
Category Order — allows you to sort categories in sidebar
Disable WP Update — turns off pesky WordPress 'update' feature
Favicon Rotator — Embeds favicon, rotates multiples
Google Analyticator — makes hooking up with Google Analytics easy
Last Modified Timestamp — sorts main list by last modified date
List Category Posts — automatically lists posts by category on page
MultiPages Widget — multiple page listings in the sidebar
My Link Order — allows you to sort links in sidebar (theme depending)
Page Links To — redirects page to web site
Search and Replace — does a global text search & replace
Search Everything — much better search feature
Search Unleashed — another search replacement to try
Show Last Edited — displays last 10 edited posts
Simply Show IDs — Lists ID numbers of posts, pages & categories
Sitemap Generator — lists all posts & pages
TD Word Count — gives total word count of pages & site
TinyMCE Advanced — additional functions for the stock editor
WP-Optimize — compresses database
Slideshow Gallery Pro — Decent slideshow program
FLV Embed — streaming FLV video player
JW Player — In case FLV Embed doesn't work
Yahoo Media Player — MP3 player with selectable playlist
Weather Widget — puts local temperature in sidebar
WP Forecast — puts full weather info & forecast in sidebar
Bookmark — sidebar link so people can bookmark your site
Random Ads — places random ads in sidebar
Let It Snow — puts snowflakes on screen
Theme Switcher Reloaded— lets reader select theme
WP-chgFontSize — lets reader change size of text
qTranslate — lets readers select between languages
ieSpell — not an actual plugin but an excellent spell-checker for IE
A big stash of plugins is here.
Stopping Plugin Updates
I've seen a few cases where a plugin stopped working after an 'automatic' update'. 'Broken Link Checker' is a perfect example. Worked fine for years, hit version 0.9 and bam! Stopped detecting broken links.
The 'trick' is to raise the version number of the last good version so WordPress will compare the two and figure you have the most recent. In the case of 'Broken Link Checker', I merely changed it from '0.8.1' to '2.8.1' and that did it.
Open the Plugin Editor, select the plugin from the drop-down menu and hit 'Select'. If you don't see a 'Version' number near the top of the page, try another from the sidebar.