More often than not, I send a photo (or other item) for a celebrity to sign. I feel that this increases one's chances of success -- especially with tough celebrities. I'm surprised at how often I get my photo back signed, as well as another signed photo provided by the celebrity. It's nice to get an extra. Perhaps the celebrity appreciates the gesture of providing a photo and rewards the writer with a little bonus?
On the same note, almost always I include a couple of blank index cards with my requests. Very often these will come back signed. These are excellent for building cast or group items later on. I also like to send signed cards as a "thank you" to fellow collectors who help me out with information or tips.