AK Notepad
Extremely useful app for storing notes in. Includes features to easily share notes with others.
Astrid
Spectacular to-do list app. Ability to synchronize with rememberthemilk.com so you’ll never lose anything. Tags allow for easy categorization.
ASTRO File Manager
Manage your files directly with this app, rather than just when you have your device hooked up to a computer with a USB cable.
chompSMS
The built-in SMS message app works alright, but the interface is not all that special. chompSMS has chat style conversation bubbles that are far more ideal for such communication.
Gmote
Make your android phone function as a remote control for your computer.
Google Sky Map
View the constellations clearly. Changes the view based on your GPS coordinates and the angle at which you hold the phone.
Google Voice
Send text messages to other Google Voice users for free. Setup customized voicemails based on who is calling you. Even allows for transcripts of voicemail, although this particular feature has a lot of room for improvement still.
handyCalc
Allows for multiple, independent calculations simultaneously and is far less limited than the built-in calculator.
Locale
Setup auto-triggers on your phone based on your location, time of day, calendar events, battery level, etc.
NewsRob
RSS reader that syncs with Google reader
Pandora
Pick an artist and listen to their songs for free and songs from similar artists.
Places Directory [No Longer In The Play Store]
Find what you’re looking for near your GPS coordinates by general category.
Shazam
Never again be stuck wondering what artist/song was just on the radio. Use Shazam to record it and report this information to you.
ShopSavvy
Scan the bar code of a product and compare prices from all over the place.
The Weather Channel
Weather information on the go with alerts.