Wow. This thread has made my day. I've downloaded at least 30 new apps I'll be killing my battery tonight trying.
As fro my favorite 5 apps, pretty much all of them have been mentioned, but I may as well repeat them for the sake of not letting them be overlooked.
1. LauncherPro -- Fully customizable home launcher replacement with up to 7 home screens and even a quicklaunch dock. Free (beta), along with the ability to add extra icons on home screens, and doesn't slow my Droid down or deal with ANY force close issues like I did with Helix2.
2. Bloo -- Facebook app with much more features and better, more reliable notifications than the Facebook for Android app.
3. Google Voice -- Voicemail inbox replacement that will transcribe voicemails into text sent by email or SMS text, free SMS text messages, cheap-ass international calling, and my own personalized number linked to my cell, home and work phones. This has literally replaced just about everything I do phone-wise on my phone. I love it.
4. SMS Popup -- I've tried and HATED Handcent and ChompSMS because they completely rip the iPhone messaging look, and offered the ugliest "customizations" to look like the native Droid Messaging app. For starters, the native app is rather customizable in itself. The only thing it lacked for me was a popup notification. SMS Popup does that for me, as well as customizations to show or hide message contents, as well as the option to read the message through TTS.
5. Swype -- Beautiful, beautiful keyboard. Shapewriter was way too clunky for my tastes, and after I found Swype, I almost don't use my physical keyboard anymore which was what sold me on my Droid over the Incredible. Beta has reopened, but only for a limited time, so hurry to
beta.swype.com and register before you have to hunt down a leaked beta.
Some other apps I use that shouldn't be left off the list are:
AppBrain -- A nice replacement to Market that has better organization, and the ability to browse the market on my computer and send to my phone.
AndChat -- An IRC client.
Astro File Manager -- Well, the name of the app says it all.
Mobile Banking -- By Bank of America
Dolphin Browser HD -- A-MAzing web browser.
Happy Hours -- Another Yelp! or Foursquare type app only featuring bars and restaurants in your area with happy hour specials. Any social alcoholic's dream.
ShootMe -- another screencap app like Drocap t hat can run in the background. Shake your phone and it will take a screenshot and save it onto your SD card.
Yelp!. Search for local restaurants, bars, shops, and (my favorite) gas stations by location. Offers user reviews and ratings. A life saver when my low fuel light is on or I need to make a last minute decision to go out somewhere.
All apps I've mentioned (except Swype) are available in Market, and all are absolutely free.