I've been asked by a few people for recommendations of Android applications that I use.  I've made a few lists, but this one is the most comprehensive of those lists.  Most links below go to Androlib which have QR codes for you to scan with your phone.

• Advanced Task Manager (free) - Great for killing hanging processes and keeping yourself from needing to reset the phone.
• Astro File Manager (free) - because everyone needs a file manager
• BookmarkBR (free) - Backup utility for your browser bookmarks.
• CalWidget (free) - Quick at a glance widget for home screen.
• Documents To Go Full ($29.99 $14.99 for a limited time) - Kinda spendy, but great if you need to open/edit docs or spreadsheets or view pdfs on your phone.  I've done a few homework assignments in a pinch with this, very handy to have.
• Draw! (free) - Great drawing app to entertain kids with.
• Foursquare (free) - Great app for checking in and letting the world know where you are, much, much better than their mobile website.  You can view offers and other foursquare specific things within the app.
• FxCamera (free) - My wife loves this because she can make "polaroid" pictures with it.
• GDocs (free) - Great if you need offline access to your google docs. Allows editing of Google Docs and quick access to Google Spreadsheets.
• Google Voice (free) - Great app for checking your Google Voice messages.  Its also great that it can take over your phone and make calls as your Google Voice number.
• GPS Status (free) - Get better information from the GPS radio, compass included.
• Live Bookmarks (free) - A great desktop widget for quick access to all of your browser bookmarks.
• Reveal Reader (free) - A simple scripture reader for for those interested in the LDS Standard Works, and other church-related publications including hymns.  Support for bookmarking and in-app downloads, so you don't have to go hunting for the files yourself.
• Ringdroid (free) - customize mp3 on your phone and make them into ringtones 
• Seesmic (free) - Great for twittering, nice big compose screen, integration with the share menu and it doesn't have a huge footprint.  Twitter updates come in pretty reliably, yfrog/twitpic/etc image preview saves time.
• Shazam (free) - Good for identifying songs on the radio or elsewhere.
• Skydeck (free) - Great if you want to keep a backup of your messages and calls on the web, check out their check out their site.  Their app also has a caller id function that identifies calls from people not in your contacts.
• TextEdit (free) - Small little application lets you jot down notes, w/o internet access.
• Voice Recorder (free) - Record audio and email it.
• Yelp (free) - Great for finding a place to eat.