This can be done by editing the LaunchToolbarConfig.xml file in the LANDesk ServiceDesk Console directory (normally C:\Program Files\LANDesk\LANDesk ServiceDesk\...).
Example - Hiding the USER entry in the dropdown:
Open the file and comment out all entries between <LaunchToolbarConfigType> and </LaunchToolbarConfigType> inclusive, where the <classname> entry is User, using the comment brackets <!-- and --> as follows:
It is strongly recommended that you take a backup of the LaunchToolbarConfig.xml file before making any changes, and restore it immediately if you see any unexpected behaviour.
Please also note that this XML file is local to all installations of Console, so in order for the change to be reflected on all clients the file would need to be edited on each one, or redeployed as necessary.