The formal wording is:
The favor of a reply is requested by May 16, 2007

The less formal is:
Please reply by May 16, 2007
or
Kindly respond by May 16, 2007

And then you call them, because some people won't reply, no matter how obvious you are. Also, I would put a date 5 days earlier than you actually want responses by.

Many people (let alone children) aren't going to RSVP no matter what. You're going to have to hit the phones like sue36 said.

:-(

I just sent bridal shower invitations and included my phone number AND my email address for the RSVP.

I received WAY more emails than phone calls, so that might work for you. It's very easy for everyone to shoot off an email!

It might help if you complile a list of your guests email addresses because that way you can email those you don't hear from!

Great ideas all. Thank you very much!

I have MUCH better luck when I include an email address for RSVP (and I know I prefer to RSVP that way instead of phoning!)

Another vote here for E mail and also think of Text responses.

We're a week post-party now, and you all were right: email worked as the best response method. My daughter heard from almost if not everyone and the numbers were fairly accurate. Thanks, everyone!
Erin