Locale is the only real Must Have that I've found so far. It's incredible, cool and highly practical.
Pandora is a good one for music fans.
PDANet will let you use your Droid as a modem for your laptop. For free. I get about 2.4mbs with it. I hear that T-Mobile won't let you run it, but Verizon will.
My Tracks is good for hiking and such. Haven't gotten to practically use it yet, but it looks pretty cool.
Handcent SMS is a great Text Messaging alternative. Beats the heck out of the proprietary one.
I'm going to amend mine a bit since it's been a few weeks since:
Still on my list -
Pandora
PDANet
MyTracks - had the chance to use it and, while a little buggy, I think I know what caused it and really like what it does. Great app.
New on my list -
Weather Channel - like the ease of use and, since I drive a lot, the ability to get the weather for "My Location" at any given time. Very cool.
Sports Tap - I use this often since I've quit watching as much on TV. Great way to keep up with any sport.
MixZing - I don't use MP3s a lot in favor of Pandora or my XM/Sirius radio, but when I do, I really like this app.
I know, that's six, but so what. I had removed HandCent not because it's not good, but I just don't text that much for it to make a big difference.
Honorable Mentions:
Dolphin Browser
Live Scores
USA Today
USA TV Guide
Shop Savvy
Sync My Pix