Useful apps that the average person would enjoy:
1. Handcent SMS
This should be installed on every DROID phone that is going to send/receive any kind of messages! This app solves a lot of problems that the basic messaging features on the phone lack. You can add contacts to a composed message using groups of contacts, or by selecting individually from a contact list. Allows you to pull the attachments out of all your messages on one easy screen, as well as individually per message. Makes it easy to grab those pictures or audio files or ringtones people send you. Supports so many other features that I won't list them here.
2. ShopSavvy
Way better than "Barcode Scanner"
3. Shazam
Identify playing music by holding the phone near the music. (Artist/Album/Song names)
4. Pandora
Online streaming music radio based on the type of music you prefer. As you listen and rate songs good/bad, the station plays songs more accurate to your taste. Excellent replacement for standard radio. Hook up a FM transmitter and your good to go in the car too (remember DROID uses standard headphone jack, which is awesome for compatiblity).
5. Power Management Widget
I think this actually comes pre-installed because I don't see it in the main slide out window. Go to add a widget and it says "power" something. Lets you change screen brightness, blutooth, wifi, gps on and off. Good for quickly adjusting the screen brightness to save power. I usually turn the brightness all the way down indoors, then back up when im outside.
I have other small things on here but these are 5 good apps that could offer a better experience for the average DROID user. I have only had my droid for 2 days now, so im sure there are plenty of other great apps out there.
Oh, and all the apps I mentioned are free in the market. As of right now, I consider Handcent SMS to have been the most useful of the apps I installed. The stock messaging interface/features are really horrible. This app makes the phone what it should have been like to begin with, and more.