you can setup cell A1 to decide if the macro should run.
info about events :http://www.cpearson.com/excel/events.htm
but will work only when you change the value in cell A1,it will not fire when a formula result changes, so this means it will work the same way
How do I run a macro every time a certain cell changes its value?

There is an event called Worksheet_Change which is triggered when a value is entered (it will not fire when a formula result changes). One of the arguments to this event is 'Target' which is a reference to what changed. Since this event will occur whenever a value changes - you can use the target to see if it is the cell you are interested in:

Private Sub Worksheet_Change(ByVal Target As Range) If Intersect(Target, Range("A1")) Is Nothing Then Exit Sub Else 'Do whatever you need to do... End If End Sub

I don't know anyone who does this, except maybe, you...
Most of the people i know, between double click and enter, is typing data, or writing formulas...

Another idea for you is to run your macro every 30 seconds, or less ...

Sub CopyFormulaResults()
Application.OnTime Now + TimeValue("00:00:10"), "CopyFormulaResults"
Range("H10:H50").Select
Selection.Copy
Range("I10").Select
Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks:=False, Transpose:=False
Application.CutCopyMode = False

End Sub