I absolutely agree, this would be very useful. Sometimes there are tricky ways to get it to run once depending on what you're doing, but it takes sacrificing a built-in priority slot (or maybe some other type of field) and an extra step that can be a pain. Consider doing something like this:
Step 1.) Change your P5 priority, call it "Ticket Received", "Unassigned", or "Not yet prioritized" or whatever makes sense to you (you can't create a new priority because you have to use built-in priority levels in triggers).
Step 2.) Change your default priority to P5 so ALL incoming tickets that have yet to be assigned will be P5.
Step 3.) Now add an extra qualifier in your trigger:
Priority level is equal to P5, check that ALL conditions must be true. Set up the rest of the trigger as desired.
Now, when a ticket comes in, it comes in at P5. The technician will do whatever the cause of the trigger is (assign a new priority, or assign a customer, etc) and that will trigger the action for the first time. Then the technician will assign the priority as appropriate and thereafter any time the trigger WOULD have been applied, it doesn't get re-run because the extra qualifier of P5 is not met.
Not an ideal workaround but it can work and be worth the effort, depending on what you're doing.
