Essential Android Apps

CyanogenMOD
Already provides most essentials in the ROM image, including:

• ADWLauncher
• Power Control Widget / Torch  - widgets that let you turn on/off various wireless radios or activate airplane mode.  I use the LED as a flashlight much more often than as a camera flash.
• Google Maps Mobile / Navigation / Street View
• Facebook / Twitter - these are internal memory storage hogs, I kinda wish I could remove them
• News & Weather - well, really just weather.
• QuickOffice
• ROM Manager
• Sound Recorder
• File Manager

Reference

• Wapedia 
• FBReader - hoping this supports the Palm Plucker format someday so I can use it with Sunrise-Desktop.
• Goggles - also does OCR and auto-translation of text that you photograph!
• Google Translate
• Barcode Scanner / Shopper - UPC code lookups and online price comparison
• Amazon
• CraigsNotification

Network

• ConnectBot - SSH client
• AndFTP
• AndChat - IRC client (though I usually just use SSH to a screen session running irssi)
• androidVNC
• Barnacle Wifi Tether - turns phone into an open HSDPA wifi hotspot
• Opera Mobile - for websites that the built-in browser can't handle.
• Dolphin - nice full-featured browser for beefier phones than mine.
• Yahoo Mail
• Yahoo Messenger  - also has a video chat addon, but haven't successfully tested that yet
• Google Chat
• Google Buzz - more useful than Twitter, esp. when used with location-aware Google Maps
• StumbleUpon - when you're bored of the web
• Blogger-droid - when your thoughts don't fit in a tweet.

Personal Digital Assistant

• Evernote - web-based notes
• Dropbox - syncs files between PCs
• KeePassDroid - encrypted keyring
• GTasks - Todo list sync'd with your Google Calender todo.
• Draw and Share - Best drawing app, easy way to roll your own lolcats
• Mileage - Track vehicle gas mileage and maintenance record
• TripIt - email your travel itinerary to them and they'll show you everything in an easy to track format
• EboBirthday - HappyDays list of the birthdays recorded in your Google Contacts / Facebook friends.
• Google Voice - Transcribes phone messages for you, also lets you send free SMS messages without having to shell out extra for text plans.

Navigation

• My Tracks - saves your GPS track and exports them to view online or in Google Earth
• Layar - augmented reality!

Utilities

• Titanium Backup - backs up all your apps to your SD card, which you then presumably back up to a computer somewhere.
• Tricorder - Star Trek interface to your phone's various sensors.
• Wifi Analyzer - shows all the wifi access points around you and helps choose a channel with the least interference.
• Compass - uses the magnometer, corrects for local variations, and points the way to waypoints
• gStrings - Audio tuning app.
• GPS Status - shows where all the satellites are and your precision based on reception quality.
• Ultimate Stopwatch
• Metal Detector - uses the magnometer to find ferrous metals.
• Droid48 - HP 48GX emulator, probably the best fully-featured graphing calculator app available to date.
• RealCalc - simple scientific calculator
• Speed Test - Measure your available bandwidth over the cell or wifi network.
• Bubble - uses accelerometer as a level.

Media

• Winamp - best streaming radio app, and should support wifi sync with your music collection
• Camera 360 - nicer effects than the built-in camera.
• Photoshop Express - retouch photos, enhance dark photos.
• Ustream Broadcaster / Viewer - share / save your streaming video in near-realtime (~10 second lag)
• BestTube - save videos from youtube onto your device for later viewing
• JustPictures - nice photo viewer, includes Flickr / Facebook / Picasa sources
• Floating Image - same as above, but also uses a neat thumbnail scroller
• Solo Lite - guitar chords. Fun way to crank out simple tunes
• Musical Lite - metronome and virtual piano / keyboard / drumset

Games

• Angry Birds
• Sketch Online - pictionary on the internet
• Chess Online
• Head 2 Head Racing - relaxing top-down racer that focuses on the technical aspect of following the ideal racing line
• X-Plane - Very nice flight simulator, but still waiting for Austin to complete the Android port.
• Bonsai Blast
• Zombie, Run! - Use your GPS to run through a horde of zombie icons that chase you.