If Hashem is perfect and unchanging, how can we pray to Him to have mercy on us? Doesn't that imply a change?
I've heard it implied that the way this works is that the prayer itself has the effect of attracting the Midah of mercy to ourselves, but that would not seem to be the poshut pshat in so much of our prayers, which are of a variation of "Please see the bad situation we're in, we're in total trouble, therefore, please have mercy on us and save us".
EDIT: several contributors have suggested that praying changes oneself, and it is this change which makes one deserving of what he's asking for. My problem with that is that the prayers I mention above seem to indicate otherwise.