Here are my favorite Android Apps that I use on my Motorola Droid. I will try and keep this list updated as better apps appear.

cyanogenmod 6.1 – community-based distribution of the open-source Android OS
launcherpro – my current home replacement
weatherbug – puts the temperature in the notification bar
vignette – camera app
tweetdeck – my twitter client of choice
handcent sms – txt/sms
gmail – where my email lives
barcode scanner – what I use to scan QR codes
ourgroceries – list app that can sync with other users
scanner buddy – listen to police, fire, and ambulance conversations in your area
google voice – voicemail
bible – youversion bible
shootme – screen capture app
setcpu – overclock your processor
appbrain – browse and install apps and wallpaper from the browser
titanium backup – weekly backups to sdcard
mybackup – easy way to restore settings and apps after switching ROMs
sms backup – backs up sms messages to gmail
wordfeud – a fun multiplayer scrabble clone
angry birds – really fun crush the castle – clone
google reader – for reading all the rss feeds I subscribe to
kindle for android – reading through my first book on the kindle app

Other Android Lists
cmcarson
lifehacker