I came across the request for this from a client I was working with. The client pointed me to some research he found on web (one link from MSDN and another from another blog). After some reading and further research, I found a great post that walks you through doing this.
Essentially, the solution is to wrap the SiteActions control with a SPSecurityTrimmedControl in the master page. The only trick to this is identifying the appropriate permission string to use for the control so you do not remove the menu from users who will actually need to use it. The string can easly be composed after reviewing the set of users (or a group of users) who will need access and checking the rights associated permission levels granted those users (or group).