"Our Groceries" is probably in my top five. It's a cloud-based grocery list (or whatever list), that multiple people can access, so both my wife and I can add things that we need to one list, and then easily check things off as we get them next time one or both of us go to the store. We also use it to keep track of movies that people suggest to us, things we need to do around the house, and whatever else we might need to keep track of.
Another good one is WidgetLocker, which requires root, but it allows you to fully customize your lock screen with widgets, app shortcuts, backgrounds, and other fun stuff.
Widget Locker doesn't require root. I'm not rooted and use it. To that I'd add their flashlight (paid) app so you'll have a flashlight right at your lock screen (use their widget, not the app).
ColorNote is nice; it lets you put a "post it" on a screen.
I use Apps Organizer (others use Folder Organizer). You create a label (like "Tools") and put all the apps that fit that description there. That way you have access to several apps, but need only one space.
Beautiful Widgets is good as you have access to your calendar and weather quickly.
Definitely color note. I have 3 stickies on my homepage, each taking up a 1x1 spot, for "Grocery List," "Simple Reminders," and "MUST BE DONE BY TODAY"
I've also used an app called Where since my Droid Eris. It's basically a "look up anything around you" app, and though there are a few these days, Where was one of the first. And even with Jeannie or google search or google maps or whatever available, whenever I'm lost or almost out of gas, want to know where to get the best local chicken wings, or even trying to remember that Chinese place near me, I always find myself going to Where. Hasn't let me down yet.
Colornote works great to store various lists, to-do, etc. You can create a widget pointing to a list.
OI Safe is a decent free password vault.
Not every-day use, but torque talks to a blue-tooth module that plugs into your car OBD diagnostic port, allowing you to read and reset engine trouble codes. Also can measure HP, torque, 0-60, etc.
Scanner Radio allows you to listen to police scanner feeds in your area (or anywhere in the world there is a feed provider). Note that the availability or audio quality depends on the feed provider, not the application author.
Flighttrack is a must for tracking plane flight status.
Droidlight (and others) give you a decent flashlight using your camera led.
Wifi Tether - My ISP since I live in BFE
Go Weather - 8 Day forecast, hourly temperature updates, live wallpaper
Pandora Radio - Gym workout soundtrack
FM Radio - When I want to listen to TV at the gym
Netflix - Watch movies
aDownloader - Torrent Handler for Android (WARNING: Drains battery in 2 hours for large files)
Battery Monitor Widget Pro - Logs and Graphs Battery usage, temperature, etc
Titanium Backup Pro - Saves precious data for my modding habit
VCast Song ID - What's the name of this song????
Go Launcher EX - Hide/Group Apps, scrolling dock, 3d home screen transitions, Icon replacements
AdFree Android - Ad Blocker
Handcent SMS - Quick reply of texts from any app
System- Gives information about the CPU, battery, storage, etc. You can have it monitor and give history. DiskUsage- Just shows you all your files in terms of size. See what's taking up a lot of room. GPS Status- Compass and which satellites are being used. Screen Grabber- Can do a screen shot without having to be rooted Switch Pro Widget- Similar to the Power Control Widget, it allows you to customize to control up to 8 things from a list of 25 On Call End- When it's active, when you end a call you have a choice on what you do after. I have it set to Homescreen, rather than call log. WiFi Analyzer- Gives the strength of the WiFi around. WiFi Finder- Scans and shows on a map the nearest WiFi hotspots. Battery Circle- Shows battery level in single digits. It sits in the notification bar so it doesn't take up any real estate on the homescreen. When you pull the bar down it shows voltage, temperature and how long unplugged.
Four new ones (for me) that I'm trying out are: Open Signal- Shows the signal strength in percentage, as well as dBm. Has pointer and map to show where the cell tower is. Smart Tools- Lots of different tools available for measuring, plum line, acoustics, etc. 4 suites for .99 cents each or all 4 for $2.50 GPS Esentials- Compass, hiking and other things with GPS Phone Info- Easier to use than typing *#*#4636#*#*