Excluding the apps included with stock Droid, like Gtalk and Gmail, here's my list in no particular order:
1. Autokiller - The best of all memory managers for rooted users.
2. Listen - Gotta have my podcasts!
3. Astro File Manager - Self explanitory.
4. SetCPU - The only way to overclock!
5. Wired/Wireless tethering for Root users - Need I say more?
6. Seesmic - The best Twitter client for Android
7. ROM Manager - Flash anytime you want and backup your system with ease.
8. Dictionary.com - Love the word of the day.
9. Dropbox for Android (official beta) - Makes transferring files to/from my Droid very easy.
10. Ringdroid - I love being able to make a new ringtone whenever I want without using my computer.
Advnaced Task Manager keeps my battery life up pretty well, not sure what I'd do without it. Also, I always play Klondike Solitaire. I think those are two that I'd miss the most.
Dolphin browser: of course.
Blizzard battle net authenticator: for those wow players.
Appmonster: app backup and manager.
Buzz deck: great news streamer app.
Weatherbug: when you live in colorado, you need to know weather every day haha.
All Google Apps (Maps, Sky Maps, etc.)
Astro
Barcode Scanner
youversion.com
Corporate Calendar/Corporate Directory (syncs with Exchange, and is free)
NFL Mobile
OurGroceries
Pandora
Shazam
ShopSavvy
SMS Backup
Swype
1: Google Maps with Navigation
2: Calorie Counter by Fat Secret (has helped me loose 50 lbs so far this year)
3: Buddy Runner (awesome tool to mark your run progress)
4: ColorNote (because Android has no Notes or Task app)
5: Google Earth (helps me plan my summer vacation to the Gulf Coast)
6: Weather Bug Elite (because the weather effects everything)
1. Seesmic (Manage more than one Twitter acc't)
2. Beautiful Widgets
3. xScope Browser (love the tabs)
4. Handcent SMS
5. HelixLauncer
6. WeatherBug Elite (I live in OK...weather changes quick)
Most deffinatley has to be the wether and toggle widgets donate version. I love the way I can tap on the weather info and it launches my radar program (rainy days).