Yes, I'm using a Droid
I bought a Droid the first day it was available. However for a sense of perspective on my comments that follow, please understand that I was migrating from a Palm Treo 700P running Chapura's KeySuite software to sync with my Outlook at work. For those unfamiliar with KeySuite, it used proprietary databases but synced perfectly with Outlook. As such it was a very good system for implementing GTD-like productivity from the Outlook platform using sync technology to the smartphone.
However, I felt that the Palm platform was slowly dying and that I was missing some of the nice new features on "always connected" devices like the iPhone, Palm Pre, or Android phones. When Verizon ventured into this space, I jumped on board.
I must say, the environment (regardless of whether it would have been an iPhone, Pre, etc) was for me a total paradigm shift from "working locally then syncing". Actually on the "working locally" front, I still think many of the hardware/software features of the Treo with KeySuite were actually more agile, but I'm rapidly adapting to this new environment.
Now, on to your question of GTD or GTD-like systems on the Droid .. .. ..
I certainly haven't found them all, but there are a number of candidate apps that seem to fall into two broad categories - those that sync with some web-based task manager and those that don't.
Remember the Milk (RTM) has it's own Android app, but you must subscribe to the RTM upgraded service ($25/year) for it to work (after a 15 free trial). Astrid and TooDo also sync with RTM. TooDo also syncs with Toodledo.
Any of those (except the RTM app itself) apps can also be used stand-alone if you like them and choose to do so.
Two notable stand alone Android apps are ActionComplete and Shuffle. Both are definitely GTD based in their approach. I tried both and chose ActionComplete.
ActionComplete entries fall into one of 4 categories:
Actions (e.g. Next Actions)
Waits (e.g. Waiting for)
Projects
Pending (e.g. Someday/maybe)
Projects can have multiple actions associated with each. Projects can also have Waits associated with them. Any entry can be "transformed" into an entry of another type. The software also utlizes tags, locations, contacts, due dates, reminders and notes for each entry type. While it doesn't sync with any web service, there is a local backup/restore function.
Action complete also has an ancillary app called AC Inbox. This app allows your to capture voice memos, typed memos, photos, or video clips with as much or as little ancially info as you choose for later processing. You can process an item into ActionComplete as any one of the ActionComplete entry types.
Overall this system is pretty fast and agile and very dedicated to GTD methodology.
Hope this helps.