The method of changing the order of the TabSheets in a PageControl in Delphi is not obvious. Apparently there is no drag and drop support (at least not in Delphi 2007). You have to change the PageIndex property. So, if you want to insert a new page, add it and then change its PageIndex to the insert position.
I smell an opportunity for a new GExperts Expert. Any takers?
EDIT: As Moreno Zenaro pointed out in a comment to my Google+ post, there is actually a GUI way of changing the order: Drag the TabSheet in the structure view.