Apparently with Android 2.3.4 and 3.1 one can now access USB accessories.
I have a Ardupilot Mega (based on Arduino) board with a USB cable connected to my laptop, a
Unfortunately the library from mik3y's answer (see here: mik3y/usb-serial-for-android) seems to be long dead. It has many problems and waiting pull requests. Also the LGPL licence prevents anybody to fork it and maintain it.
But don't lose your hope, there's a working replacement and it's under the MIT licence. felHR85/UsbSerial.
EDIT: I found a maintained fork of mik3y's library. But the licence or readme is not updated, so I suppose the owner doesn't have a connection to mik3y and simply took it and improved it. I hope he won't get into any trouble because of the licence, because we need this library. See kai-morich/usb-serial-for-android
EDIT2: It seems that all of these libraries are maintained again, mik3y joined forces with kai-morich and they're working together now.