For a Computer Science Information Warfare class a few years ago I wrote a python script that ran on libpcap promiscuous packet capture files to parse out facebook chat traffic (earlang tuples passed in clear text), and thought an interesting project would be to port the program to Android.
I would like to rewrite it in Java but can't find any information about packet capturing directly on the handset.
As far as I'm aware, there is no way to put the Wifi NIC into monitoring mode from the public API. However, depending on the device used by the phone, you may be able to get the system to put it into monitor mode if you have root access.
Take a look at the code in the android-wifi-tether project:
http://code.google.com/p/android-wifi-tether/source/browse/?r=304#svn/trunk%3Fstate%3Dclosed
There are some Linux binaries and config files in the res/raw/ directory, which are copied into place and controlled by the app in Java.
Remember that you will need to root the phone for this to work.