Unfortunately, after only one week, my Curve refused to charge! I tried reinstalling the drivers and using the car charger, neither of which helped. I was getting ready to throw in the towel and contact AT&T for a replacement when I stumbled across this helpful post on the Blackberry support forums.
It turns out that the mini-USB connector on the Blackberry is very susceptible to getting out of alignment just enough that it won't charge. I employed the recommended screwdriver technique from the article to gently bend the connector back into alignment, and I was charging again in no time.
So if your phone (or other device) that relies on a mini-USB port for charging won't charge, give it a try!
While I'm on the subject of Blackberries, if you have one with a full keyboard, then you are really missing out if you haven't enabled keyboard shortcuts. To enable them, go to Phone, Options, General Options, and set "Dial from Home Screen" to "Off". Now you will be able to launch common tasks with a single keypress from the home screen, such as "M" to view your messages or "W" to launch the web browser. More details on this useful Blackberry 101 Beginner's Guide.