How can you just pick 5???
Best Task Manager: I've tried 5-10 of these puppies, and while Advanced Task Killer (Free) is no slouch, I def have to go with Automatic Task Killer. Great battery life, easy interface, limited/no ads, and 2 great widgets.
Games: Thanks to this thread I discovered Cestos = the BESTos!
Homerun Battle 3D is also amazing and has great multi-player online play.
If you haven't tried NESoid with the Wii Controller functionality you are seriously missing out. I simply dock my Droid in landscape and play Super Mario Bros. 3 with my Wii controller wirelessly. 'Nuff said.
I also suggest Bubble Defense, Robo Defense, Toss It, and Phit Droid!
Productivity: Adobe Reader, ASTRO File Manager (doubles as great back-up app,) Documents To Go (Full - well worth $9.99,) Dropbox (wireless file syncing to the max,) Evernote, GDocs (great for people who use Google Docs,) Jorte (beautiful agenda/calendar replacement app,) Mint.com (MUST HAVE,) OI Safe, and USA Hot Jobs (The answer to the unemployment rate? Android users able to change the world!)
Music: gStrings (amazing app for tuning guitar or whatev,) Listen (best podcast app hands-down,) Music Wizard (the Limewire of Android,) Pandora, Slacker, and SoundHound (sorry Shazam!)
For Root Users: ROM Manager, AdFree, Root-Ed ShoutBox, SetCPU, Spare Parts, and Wireless Tether...
Reading: Kindle, NewsRoom, and the best Bible app - KJV Bible (Search "talking Bible." It has more than just the KJV, but is amazing. Must try.)
Utilities: Uninstaller, Scientific Calculator, Calorie Counter, Craigsnotifica (Craigslist app,) Dictionary.com, Goggles, Google Translate, Google Sky Map, HistoryEraser, IMDb, Kayak (for traveling, flights, hotels, etc,) myLock Prefs (so your phone automatically unlocks - amazing,) Recordoid (MUST HAVE VOICE RECORDER,) TeslaLED (camera flash = flashlight - w/ great widgets,) Timeriffic, and Vlingo!
Entertainment: Epic Fail, Gowalla, Mario Soundboard, Tapatalk Pro, TV.com, and Ustream Viewer.
Backgrounds & Ringtones: Zedge and Backgrounds...
Photography (Huge hobby of mine...): FxCamera, PhotoFunia, Picasa Tool, PicSay Pro, Retro Camera, and Vignette. I take professional-quality pics on my Droid with these software(s)...
Weather: WeatherBug Elite - no question. Unrivaled widgets, accuracy, features, etc.
Browser: apart from my stock Chrome browser with Adobe Flash, I recommend the newest SkyFire - much improved.
Miscellaneous: Android Central widget (of course,) Runstar, ScoreMobile (best sports app - period,) ESPN ScoreCenter, Shopper (by Google,) Where, Google Voice, tumblroid, and MY FAVE TWITTER APP (for the last couple days, anyway)... SEESMIC! (Gotta love that raccoon! And the free window decals they sent me!)
If these seem like a lot (or overwhelming,) please know I have all those and MORE installed on my Moto Droid running ChevyNo1's Simply Stunning 4.3 overclocked to 1.25 GHz on Android 2.2! Runs smooth as butter and quick as greased lightning. No complaints here. Feel free to ask me any ?'s regarding any of my choices. For the record, I have personally purchased and tried EVERY Twitter app on the Market - so don't hesitate to ask me anything (or tweet me @a_googler!) Thanks all!