Is is possible to list the members of a Facebook group using the Facebook API? If yes, how?
First you need an access token. I'd recommend this article:
http://benbiddington.wordpress.com/2010/04/23/facebook-graph-api-getting-access-tokens/
If you want a permanent access token you must ask for the "offline_access" extended permission on getting it.
After that, it's just a matter of issuing a REST API call:
https://graph.facebook.com/[GROUPID]/members?access_token=[ACCESSTOKEN]
and you'll receive a JSON list of all the members of that group. Very handy!