If you are using Filemaker 10 or 11, then you can do this with the OnObjectExit script trigger.
But this seems only to work with one choice, what if I have 10 choices in my drop down menu and I want to link every choice to a different script action?
Use IF, ElseIF statements in your script to branch to different actions based on the value of the drop down.
If [ Table:: DropDownfield = "option 1" ]
#Do option one stuff
Else If [Table:: DropDownField = "option 2"]
#Do option two stuff
# Do option three stuff
If the user can make multiple selections you can use functions like Patterncount or FilterValues to identify which options where selected.