I'd like to see a Group Moderator feature. Basically when creating a group, you can apply a moderator to the group that can control who's in the group or not. Either by request, or invitation, with options to approve, deny, or remove.
Please do make this happen. We use it extensively to allow our users to get their own private forums on our site. Essentially, we create a new usergroup and a new subforum, and assign the proper rights to the group while denying everyone else access to the forum.
Being able to off-load the workload of administrating these groups onto someone who actually can verify whether a random applicant belongs to the group or not would be a blessing.