These are Wordpress Plug-ins I currently (or used to) use.  Some themes do these functions for you, so not all plug-ins will be useful to you.  I will try to keep this up to date as new plug-ins come out or change, so this page is a work in progress.

Engagement:

• Contact Form 7 - great for making contact forms (kind of obvious)
• WP Greet Box - adds a box at the top of posts asking people to subscribe
• Yet Another Related Posts Plugin - automagically adds related posts to the end of new new posts
• Evermore - Automagically makes posts appear as excerpts only on multi-post pages
• Ninja Announcements - Schedule and post announcements to the top of your blog

Commenting:

• Akismet - Spam Filter (you need an api key, free for small/ non-corporate blogs)
• Subscribe to Comments - Allows users to subscribe to future comments on your post
• Disqus - Provides Spam, Subscriptions and other social features to comments

Social:

• WP Tweet Button - Automatically adds the new Twitter Button to posts and pages
• Sociable - adds social links to the end of posts
• Like - Facebook like button plug-in with lots of options
• Sharebar - Adds a bar that slides down the side with share buttons (like tweet button, Facebook, etc)

Mobile:

• WPTouch - What I am currently using (free and premium versions exist)
• Wordpress Mobile Edition - Another option, uses a secondary theme file

Security:

• Secure Wordpress - Helps remove potential security holes in Wordpress
• Login Lockdown - blocks IPs with too many incorrect password attempts

Back end:

• WP Optimize - clears out crap that accumulates in your SQL database
• Tiny MCE Advanced - adds lots of editing tools to Post and Page writing screens
• Google Analytics for Wordpress - Easy to use Google Analytics integration
• WordPress Database Backup - Emails a database backup at request or schedule
• Use Google Libraries - Increases speed when using jQuery, etc. (more info)