I usually start with the truth... now I might tone it down or pick my words carefully if it's something truly horrible about the program.
If you asked them why they didn't select you, what do you think that they would say?
I found that most schools were open to discussing my weaknesses as an applicant, and a few were not.
If you really found the program annoying or not to your liking, you could say:
"Dear School X,
While I appreciate your sincere offer, I must unfortunately reject your offer at this time. Due to the high number of acceptances, I don't have the resources to discuss why each program was rejected, but be sure that I did give your acceptance full consideration before rejecting it. I rejected a number of qualified programs this year and simply couldn't accept more than one graduate program to attend. I wish you the best of luck in recruiting students in the future. I know your program will have the utmost success in its future endeavors and I am sure that you will successfully recruit students that meet your stringent admission requirements."
I don't know why you would tell them anything other than the truth, even if it's a touchy subject like not clicking with a faculty member or not enough funding. Programs like to know if their stipend needs to be more competitive or if it was just a personal choice. I declined at a school that had over half their "first choice" picks decline as well, and they wanted feedback about why their program wasn't chosen first. I told them why, and hopefully my feedback will make the program's recruiting more successful next year.