I’ve had the Droid-X since July; long enough to settle into a groove as far as applications go. These are my go-to apps; the ones I would recommend without hesitation.
Note that these apps are not all free; after spending $200 for a phone and $60/month for the phone, spending $5 for an app doesn’t bother me. My logic, doesn’t have to be yours. The links are not links into the Marketplace though most should lead you there eventually. No order or ranking implied, and the prices are merely what I found on the net.