I'd like to be able to create a trigger on the GroupMember table. One potential use case for this, if you're using Public Groups to drive any security / sharing, it may be desirable to prevent certain users from being added to certain groups. The best place to catch this is at the time the user is added to the Public Group, which is the act of adding the GroupMember record. I could easily solve this if I could catch and react to that DML.
Currently I'm left with something kludgy like a polling batch job that watches for new records in GroupMember and retroactively removes people (for my use case).