I'm really paranoid about people having copies of my keys. So, because of this, I always replace the door lock cylinder when I move to a new house.
But my paranoia doesn't end there; I save the original lock cylinder, and when someone will have access to my keys for a while (for example a friend staying for a day, someone fixing stuff around the house, etc) I switch to the old door lock cylinder temporarily. That way, if they make copies of the keys, those aren't useful since I'll switch the locks again when they leave :)
By the way, changing the lock takes like 30 seconds, in case you were wondering.